MBBS and BDS entrance Physics: NEET-UG questions on Nepal's MBBS syllabus: Waves and Optics

2013 · NEET-UG (India) · 4 marks

A wave travelling in the $+x$ -direction having displacement along $y$ -direction as 1 m, wavelength $2\pi$ m and frequency of $\frac1\pi$ Hz is represented by:
(a) $y=\sin(x-2t)$ (b) $y=\sin(2\pi x-2\pi t)$ (c) $y=\sin(10\pi x-20\pi t)$ (d) $y=\sin(2\pi x+2\pi t)$

Answer

(a) $y=\sin(x-2t)$

Amplitude is 1 m. $k=\frac{2\pi}{\lambda}=1$ and $\omega=2\pi f=2$ rad/s. A wave in the $+x$ direction has the form $y=A\sin(kx-\omega t)=\sin(x-2t)$ . Option (d) has $+\omega t$ , so it travels in $-x$ .

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2013 · NEET-UG (India) · 4 marks

If we study the vibration of a pipe open at both ends, then the following statement is not true:
(a) Open end will be antinode (b) Odd harmonics of the fundamental frequency will be generated (c) All harmonics of the fundamental frequency will be generated (d) Pressure change will be maximum at both ends

Answer

(b) Odd harmonics of the fundamental frequency will be generated

A pipe open at both ends has antinodes (maximum pressure variation) at both ends, and produces all harmonics: $f=\frac{nv}{2L}$ , $n=1,2,3,\dots$ Only odd harmonics occur in a pipe closed at one end, so the statement in (b) is the false one.

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2013 · NEET-UG (India) · 4 marks

A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is:
(a) 254 Hz (b) 246 Hz (c) 240 Hz (d) 260 Hz

Answer

(a) 254 Hz

The unknown frequency is $250\pm4$ , i.e. 246 or 254 Hz. Its second harmonic is 492 or 508 Hz. Beats with 513 Hz would be 21 or 5 per second; only 508 gives 5, so $n=254$ Hz.

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2013 · NEET-UG (India) · 4 marks

A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:
(a) $\frac{R}{2(\mu_1+\mu_2)}$ (b) $\frac{R}{2(\mu_1-\mu_2)}$ (c) $\frac{R}{(\mu_1-\mu_2)}$ (d) $\frac{2R}{(\mu_2-\mu_1)}$

Answer

(c) $\frac{R}{(\mu_1-\mu_2)}$

Plano-convex lens: $\frac1{f_1}=\frac{\mu_1-1}{R}$ . Plano-concave lens (the curved face has the same radius): $\frac1{f_2}=-\frac{\mu_2-1}{R}$ . Combined: $\frac1f=\frac{\mu_1-\mu_2}{R}$ , so $f=\frac{R}{\mu_1-\mu_2}$ .

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2013 · NEET-UG (India) · 4 marks

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:
(a) 5 cm (b) 2.5 cm (c) 1.67 cm (d) 1.5 cm

Answer

(c) 1.67 cm

Powers add for lenses in contact: $P=40+20=60$ D, so $f=\frac1{60}$ m $\approx1.67$ cm. For a normal eye viewing distant objects the image forms on the retina, so the retina lies at the focal length, 1.67 cm.

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2013 · NEET-UG (India) · 4 marks

In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths $\lambda_1=12000$ Å and $\lambda_2=10000$ Å. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?
(a) 8 mm (b) 6 mm (c) 4 mm (d) 3 mm

Answer

(b) 6 mm

Bright fringes coincide when $n_1\lambda_1=n_2\lambda_2$ : $12n_1=10n_2$ , so the smallest integers are $n_1=5$ , $n_2=6$ . $y=\frac{n_1\lambda_1D}{d}=\frac{5\times1.2\times10^{-6}\times2}{2\times10^{-3}}=6\times10^{-3}$ m $=6$ mm.

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2014 · NEET-UG (India) · 4 marks

If $n_1$ , $n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by:
(a) $\frac{1}{\sqrt n}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$ (b) $\sqrt n=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}$ (c) $n=n_1+n_2+n_3$ (d) $\frac1n=\frac1{n_1}+\frac1{n_2}+\frac1{n_3}$

Answer

(d) $\frac1n=\frac1{n_1}+\frac1{n_2}+\frac1{n_3}$

Fundamental frequency is $n=\frac1{2L}\sqrt{\frac T\mu}$ , so $n\propto\frac1L$ for the same tension and mass per length. Since $L=L_1+L_2+L_3$ , we get $\frac1n=\frac1{n_1}+\frac1{n_2}+\frac1{n_3}$ .

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2014 · NEET-UG (India) · 4 marks

If focal length of objective lens is increased then magnifying power of:
(a) microscope and telescope both will increase. (b) microscope and telescope both will decrease. (c) microscope will decrease but that of telescope will increase. (d) microscope will increase but that of telescope decrease.

Answer

(c) microscope will decrease but that of telescope will increase.

For a telescope, $M=\frac{f_o}{f_e}$ , so a larger $f_o$ increases $M$ . For a microscope, $M\approx\frac{L}{f_o}\left(1+\frac{D}{f_e}\right)$ , so a larger $f_o$ decreases $M$ . The two instruments therefore respond in opposite ways, which rules out (a) and (b).

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2014 · NEET-UG (India) · 4 marks

The angle of a prism is $A$ . One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ , of the prism is:
(a) $2\cos A$ (b) $\frac12\cos A$ (c) $\tan A$ (d) $2\sin A$

Answer

(a) $2\cos A$

The ray retraces its path only if it strikes the silvered face normally, so the angle of refraction at the first face is $r=A$ (the prism angle). Snell's law: $\mu=\frac{\sin 2A}{\sin A}=\frac{2\sin A\cos A}{\sin A}=2\cos A$ . Option (d) comes from wrongly swapping the roles of $\sin$ and $\cos$ .

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2014 · NEET-UG (India) · 4 marks

The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are: (velocity of sound $=340\ \mathrm{m\,s^{-1}}$ )
(a) 5 (b) 7 (c) 6 (d) 4

Answer

(c) 6

A closed pipe has only odd harmonics: $f_n=\frac{(2n-1)v}{4L}$ . Fundamental $=\frac{340}{4\times0.85}=100$ Hz. Possible frequencies are $100, 300, 500, 700, 900, 1100$ Hz, and the next one, $1300$ Hz, exceeds $1250$ Hz. So there are $6$ natural oscillations; counting even multiples (as for an open pipe) would give a wrong count.

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2014 · NEET-UG (India) · 4 marks

A beam of light of $\lambda=600$ nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is:
(a) 1.2 mm (b) 2.4 cm (c) 2.4 mm (d) 1.2 cm

Answer

(c) 2.4 mm

The first minima lie at $y=\pm\frac{\lambda D}{a}$ from the centre, so the distance between them is the width of the central maximum $\frac{2\lambda D}{a}$ . $\frac{2\times600\times10^{-9}\times2}{10^{-3}}=2.4\times10^{-3}$ m $=2.4$ mm. Option (a) gives only half this width, the distance from the centre to one first minimum.

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2014 · NEET-UG (India) · 4 marks

A speeding motorcyclist sees a traffic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the honk as heard by him will be:
(a) 1372 Hz (b) 1412 Hz (c) 1454 Hz (d) 1332 Hz

Answer

(a) 1372 Hz

Both move in the same direction (towards the right), the motorcyclist behind at $10$ m/s and the car ahead at $5$ m/s. The source moves away from the observer, who is chasing it. $f'=f\,\frac{v-v_o}{v-v_s}=1392\times\frac{343-10}{343-5}=1392\times\frac{333}{338}\approx1372$ Hz. Option (b), which is larger than $f$ , would need the source and observer approaching each other, which is not the case.

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2014 · NEET-UG (India) · 4 marks

In the Young's double-slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is $K$ ( $\lambda$ being the wave length of light used). The intensity at a point where the path difference is $\lambda/4$ will be:
(a) $K/4$ (b) $K/2$ (c) Zero (d) $K$

Answer

(b) $K/2$

Intensity is $I=4I_0\cos^2\frac{\phi}{2}$ with phase difference $\phi=\frac{2\pi}{\lambda}\Delta x$ . For $\Delta x=\lambda$ , $\phi=2\pi$ and $I=4I_0=K$ . For $\Delta x=\lambda/4$ , $\phi=\pi/2$ and $I=4I_0\cos^2\frac{\pi}{4}=2I_0=\frac{K}{2}$ . Option (a) wrongly scales the intensity linearly with path difference.

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2015 · NEET-UG (India) · 4 marks

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:
(a) 10.5 Hz (b) 105 Hz (c) 155 Hz (d) 205 Hz

Answer

(b) 105 Hz

For a string fixed at both ends the resonant frequencies are $f_n = nf_1$ , so consecutive harmonics differ by $f_1$ . With no resonance between 315 Hz and 420 Hz, they are adjacent harmonics (3rd and 4th), so $f_1 = 420-315 = 105$ Hz.

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2015 · NEET-UG (India) · 4 marks

In an astronomical telescope in normal adjustment a straight black line of length $L$ is drawn on inside part of objective lens. The eye-piece forms a real image of this line. The length of this image is $l$ . The magnification of the telescope is:
(a) $\frac{L+l}{L-l}$ (b) $\frac{L}{l}$ (c) $\frac{L}{l}+1$ (d) $\frac{L}{l}-1$

Answer

(b) $\dfrac{L}{l}$

The eyepiece forms a real image of the line drawn on the objective, whose linear magnification is $l/L = v/u$ . In normal adjustment the lens separation is $f_o+f_e$ , so the object distance is $u=f_o+f_e$ and the image distance is $v=\dfrac{f_e(f_o+f_e)}{f_o}$ , giving $\dfrac lL=\dfrac{f_e}{f_o}$ . The telescope magnification is $m=\dfrac{f_o}{f_e}=\dfrac{L}{l}$ .

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2015 · NEET-UG (India) · 4 marks

Two slits in Young's experiment have widths in the ratio 1 : 25. The ratio of intensity at the maxima and minima in the interference pattern, $\frac{I_{max}}{I_{min}}$ is:
(a) $\frac{49}{121}$ (b) $\frac{4}{9}$ (c) $\frac{9}{4}$ (d) $\frac{121}{49}$

Answer

(c) $\dfrac{9}{4}$

Slit widths are proportional to intensities, so $I_1:I_2=1:25$ and the amplitudes are in the ratio $a_1:a_2=1:5$ . Then $\dfrac{I_{max}}{I_{min}}=\left(\dfrac{a_1+a_2}{a_1-a_2}\right)^2=\left(\dfrac{6}{4}\right)^2=\dfrac94$ . A common slip is to use the intensity ratio $1:25$ in place of the amplitude ratio, which gives $(26/24)^2$ rather than the correct value.

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2015 · NEET-UG (India) · 4 marks

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of $19.4\ \mathrm{m\,s^{-1}}$ at an angle of $60^\circ$ with the source-observer line (the velocity of the source makes $60^\circ$ with the line, pointing partly towards the observer). The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330\ \mathrm{m\,s^{-1}}$ ) is:
(a) 106 Hz (b) 97 Hz (c) 100 Hz (d) 103 Hz

Answer

(d) 103 Hz

Only the component of the source velocity along the line to the observer matters: $v_s\cos60^\circ = 19.4\times0.5=9.7\ \mathrm{m\,s^{-1}}$ , directed toward the observer. Then $f'=f\dfrac{v}{v-v_s\cos60^\circ}=100\times\dfrac{330}{330-9.7}\approx103$ Hz. It is higher than 100 Hz because the source is approaching.

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2016 · NEET-UG (India) · 4 marks

A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of $15\ \mathrm{m\,s^{-1}}$ . Then, the frequency of sound that the observer hears in the echo reflected from the cliff is: (Take velocity of sound in air $=330\ \mathrm{m\,s^{-1}}$ )
(a) 885 Hz (b) 765 Hz (c) 800 Hz (d) 838 Hz

Answer

(d) 838 Hz

The cliff acts as a stationary observer, then a stationary re-emitter. The siren moves toward the cliff, so the cliff receives $f'=800\times\dfrac{330}{330-15}\approx838$ Hz. The reflected sound travels back to the observer from the stationary cliff, so no further change occurs and the observer hears 838 Hz. The siren moving away from the observer does not matter, since the observer hears only the echo.

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2016 · NEET-UG (India) · 4 marks

In a diffraction pattern due to a single slit of width $a$ , the first minimum is observed at an angle $30^\circ$ when light of wavelength 5000 Å is incident on the slit. The first secondary maximum is observed at an angle of:
(a) $\sin^{-1}\left(\frac{3}{4}\right)$ (b) $\sin^{-1}\left(\frac{1}{4}\right)$ (c) $\sin^{-1}\left(\frac{2}{3}\right)$ (d) $\sin^{-1}\left(\frac{1}{2}\right)$

Answer

(a) $\sin^{-1}\left(\dfrac{3}{4}\right)$

First minimum: $a\sin30^\circ=\lambda$ , so $a=2\lambda$ . The first secondary maximum is approximately at $a\sin\theta=\dfrac{3\lambda}{2}$ , giving $\sin\theta=\dfrac{3\lambda}{2\times2\lambda}=\dfrac34$ , so $\theta=\sin^{-1}\left(\frac34\right)$ .

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2016 · NEET-UG (India) · 4 marks

Match the corresponding entries of column 1 with column 2. [Where $m$ is the magnification produced by the mirror]
Column 1: (A) $m=-2$ ; (B) $m=-\frac12$ ; (C) $m=+2$ ; (D) $m=+\frac12$ Column 2: (a) Convex mirror; (b) Concave mirror; (c) Real image; (d) Virtual image
(a) A→c and d; B→b and d; C→b and c; D→a and d (b) A→b and c; B→b and c; C→b and d; D→a and d (c) A→a and c; B→a and d; C→a and b; D→c and d (d) A→a and d; B→b and c; C→b and d; D→b and c

Answer

(b) A→b and c; B→b and c; C→b and d; D→a and d

A convex mirror always gives a virtual, erect, diminished image, so $m=+\frac12$ (D) is convex with a virtual image. A real image is inverted ( $m<0$ ) and only a concave mirror forms it, so $m=-2$ and $m=-\frac12$ (A, B) are concave and real. A magnified erect image ( $m=+2$ , C) is virtual and needs a concave mirror with the object inside the focus.

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2016 · NEET-UG (India) · 4 marks

An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance:
(a) 54.0 cm (b) 37.3 cm (c) 46.0 cm (d) 50.0 cm

Answer

(a) 54.0 cm

For the objective, $u=-200$ cm and $f_o=40$ cm: $\frac1v=\frac1{40}-\frac1{200}=\frac1{50}$ , so $v=50$ cm. For normal viewing (final image at infinity) the eyepiece is placed at its focal length from this image. So the separation is $50+4=54$ cm.

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2016 · NEET-UG (India) · 4 marks

The angle of incidence for a ray of light at a refracting surface of a prism is $45^\circ$ . The angle of prism is $60^\circ$ . If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are:
(a) $30^\circ;\ \frac{1}{\sqrt2}$ (b) $45^\circ;\ \frac{1}{\sqrt2}$ (c) $30^\circ;\ \sqrt2$ (d) $45^\circ;\ \sqrt2$

Answer

(c) $30^\circ;\ \sqrt2$

At minimum deviation $r_1=r_2=A/2=30^\circ$ and $i=45^\circ$ . Then $\delta_{min}=2i-A=90-60=30^\circ$ . The refractive index is $\mu=\dfrac{\sin45^\circ}{\sin30^\circ}=\dfrac{1/\sqrt2}{1/2}=\sqrt2$ . A value $\mu<1$ (options a, b) is impossible for glass in air.

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2016 · NEET-UG (India) · 4 marks

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is:
(a) 200 cm (b) 66.7 cm (c) 100 cm (d) 150 cm

Answer

(d) 150 cm

In a closed pipe the resonant lengths are odd multiples of $\lambda/4$ . The smallest length is $\lambda/4=50$ cm, so $\lambda=200$ cm. The next resonance is at $3\lambda/4=150$ cm.

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2016 · NEET-UG (India) · 4 marks

A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda_2$ . The ratio $\lambda_2/\lambda_1$ is:
(a) $\sqrt{\frac{m_1+m_2}{m_1}}$ (b) $\sqrt{\frac{m_1}{m_2}}$ (c) $\sqrt{\frac{m_1+m_2}{m_2}}$ (d) $\sqrt{\frac{m_2}{m_1}}$

Answer

(c) $\sqrt{\dfrac{m_1+m_2}{m_2}}$

The frequency of the pulse stays the same, so $\lambda\propto v=\sqrt{T/\mu}$ . At the bottom the tension is $m_2g$ ; at the top it is $(m_1+m_2)g$ , and $\mu$ is the same. So $\dfrac{\lambda_2}{\lambda_1}=\sqrt{\dfrac{(m_1+m_2)g}{m_2g}}=\sqrt{\dfrac{m_1+m_2}{m_2}}$ .

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2017 · NEET-UG (India) · 4 marks

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that the 8th bright fringe in the medium lies where the 5th dark fringe lies in air. The refractive index of the medium is nearly
(a) 1.59 (b) 1.69 (c) 1.78 (d) 1.25

Answer

(c) 1.78

Position of the $n$ th bright fringe is $n\lambda D/d$ and of the $n$ th dark fringe is $(n-\tfrac12)\lambda D/d$ . In the medium the wavelength is $\lambda/\mu$ , so $8\lambda/\mu = 4.5\lambda$ (5th dark in air).

Hence $\mu = 8/4.5 \approx 1.78$ .

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2017 · NEET-UG (India) · 4 marks

Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s]
(a) 361 Hz (b) 411 Hz (c) 448 Hz (d) 350 Hz

Answer

(c) 448 Hz

Source and observer approach each other, so $f'=f\,\dfrac{v+v_o}{v-v_s}=400\times\dfrac{340+16.5}{340-22}=400\times\dfrac{356.5}{318}\approx448$ Hz.

Using a minus in the numerator or a plus in the denominator would give the receding-case values (such as 361 Hz), which is wrong here.

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2017 · NEET-UG (India) · 4 marks

The ratio of resolving powers of an optical microscope for two wavelengths $\lambda_1=4000$ Å and $\lambda_2=6000$ Å is
(a) $9:4$ (b) $3:2$ (c) $16:81$ (d) $8:27$

Answer

(b) $3:2$

Resolving power of a microscope is $R=\dfrac{2\mu\sin\theta}{1.22\lambda}\propto\dfrac1\lambda$ .

So $R_1:R_2=\lambda_2:\lambda_1=6000:4000=3:2$ . The squared ratio $9:4$ is wrong because the dependence is linear.

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2017 · NEET-UG (India) · 4 marks

A thin prism having refracting angle $10^\circ$ is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be
(a) $6^\circ$ (b) $8^\circ$ (c) $10^\circ$ (d) $4^\circ$

Answer

(a) $6^\circ$

For dispersion without deviation the net deviation is zero: $(\mu-1)A+(\mu'-1)A'=0$ in magnitude.

$(1.42-1)(10^\circ)=(1.7-1)A'$ , so $A'=4.2/0.7=6^\circ$ .

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2017 · NEET-UG (India) · 4 marks

The two nearest harmonics of a tube closed at one end and open at the other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?
(a) 20 Hz (b) 30 Hz (c) 40 Hz (d) 10 Hz

Answer

(a) 20 Hz

A closed pipe has only odd harmonics $f_n=(2k+1)f_0$ , so adjacent harmonics differ by $2f_0$ .

$2f_0=260-220=40$ Hz, so $f_0=20$ Hz (220 and 260 are the 11th and 13th harmonics).

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2017 · NEET-UG (India) · 4 marks

A beam of light from a source $L$ is incident normally on a plane mirror fixed at a certain distance $x$ from the source. The beam is reflected back as a spot on a scale placed just above the source $L$ . When the mirror is rotated through a small angle $\theta$ , the spot of the light is found to move through a distance $y$ on the scale. The angle $\theta$ is given by
(a) $\dfrac{y}{x}$ (b) $\dfrac{x}{2y}$ (c) $\dfrac{x}{y}$ (d) $\dfrac{y}{2x}$

Answer

(d) $\dfrac{y}{2x}$

Rotating the mirror by $\theta$ turns the reflected ray by $2\theta$ . The spot moves $y=x\tan2\theta\approx2\theta x$ for small angles.

So $\theta=\dfrac{y}{2x}$ . Option (a) forgets the doubling.

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2017 · NEET-UG (India) · 4 marks

Two polaroids $P_1$ and $P_2$ are placed with their axes perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1$ . A third polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its axis makes an angle $45^\circ$ with that of $P_1$ . The intensity of transmitted light through $P_2$ is
(a) $\dfrac{I_0}{4}$ (b) $\dfrac{I_0}{8}$ (c) $\dfrac{I_0}{16}$ (d) $\dfrac{I_0}{2}$

Answer

(b) $\dfrac{I_0}{8}$

$P_1$ transmits half of the unpolarised light: $I_1=I_0/2$ . Then by Malus's law through $P_3$ at $45^\circ$ : $I_2=\tfrac{I_0}{2}\cos^245^\circ=I_0/4$ .

$P_2$ is $45^\circ$ from $P_3$ too, so $I_3=\tfrac{I_0}{4}\cos^245^\circ=I_0/8$ .

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2018 · NEET-UG (India) · 4 marks

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be
(a) 36 cm towards the mirror (b) 30 cm away from the mirror (c) 30 cm towards the mirror (d) 36 cm away from the mirror

Answer

(d) 36 cm away from the mirror

Mirror formula with $f=-15$ cm. For $u=-40$ : $\tfrac1v=-\tfrac1{15}+\tfrac1{40}$ , so $v=-24$ cm. After moving 20 cm closer, $u=-20$ : $\tfrac1v=-\tfrac1{15}+\tfrac1{20}$ , so $v=-60$ cm.

The image moves from 24 cm to 60 cm in front of the mirror, a shift of 36 cm away from the mirror.

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2018 · NEET-UG (India) · 4 marks

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30^\circ$ . One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is
(a) Zero (b) $60^\circ$ (c) $30^\circ$ (d) $45^\circ$

Answer

(d) $45^\circ$

The ray retraces its path only if it strikes the silvered face normally. With prism angle $A=30^\circ$ , $r_1+r_2=A$ and $r_2=0$ , so $r_1=30^\circ$ .

Snell's law: $\sin i=\sqrt2\sin30^\circ=\tfrac{1}{\sqrt2}$ , so $i=45^\circ$ .

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2018 · NEET-UG (India) · 4 marks

A tuning fork is used to produce resonance in a glass tube. The length of the air column in the tube can be adjusted by a variable piston. At room temperature of $27^\circ$ C two successive resonances are produced at 20 cm and 73 cm column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at $27^\circ$ C is
(a) 300 m/s (b) 330 m/s (c) 350 m/s (d) 339 m/s

Answer

(d) 339 m/s

Successive resonances in a closed tube differ by $\lambda/2$ : $\lambda/2 = 73 - 20 = 53$ cm, so $\lambda = 106$ cm. $v = f\lambda = 320 \times 1.06 = 339.2$ m/s. Using $\lambda/4 = 20$ cm would ignore the end correction and give the wrong value.

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2018 · NEET-UG (India) · 4 marks

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is
(a) 16 cm (b) 13.2 cm (c) 12.5 cm (d) 8 cm

Answer

(b) 13.2 cm

Third harmonic of a closed pipe: $f = \dfrac{3v}{4L_c} = \dfrac{3v}{0.8}$ . Fundamental of an open pipe: $f = \dfrac{v}{2L_o}$ . Equating, $L_o = \dfrac{0.8}{6} = 0.1333$ m $\approx 13.2$ cm.

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2018 · NEET-UG (India) · 4 marks

Unpolarised light is incident from air on a plane surface of a material of refractive index $\mu$ . At a particular angle of incidence $i$ , it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?
(a) $i=\tan^{-1}\left(\dfrac{1}{\mu}\right)$ (b) Reflected light is polarised with its electric vector parallel to the plane of incidence (c) $i=\sin^{-1}\left(\dfrac{1}{\mu}\right)$ (d) Reflected light is polarised with its electric vector perpendicular to the plane of incidence

Answer

(d) Reflected light is polarised with its electric vector perpendicular to the plane of incidence

Reflected and refracted rays at $90^\circ$ is Brewster's condition, so $\tan i = \mu$ (not $1/\mu$ or $\sin i = 1/\mu$ ). Only the component perpendicular to the plane of incidence is reflected, so the reflected light is plane polarised with E perpendicular to that plane.

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2018 · NEET-UG (India) · 4 marks

In Young's double slit experiment the separation $d$ between the slits is 2 mm, the wavelength $\lambda$ of the light used is 5896 Å and the distance $D$ between the screen and slits is 100 cm. It is found that the angular width of the fringes is $0.20^\circ$ . To increase the fringe angular width to $0.21^\circ$ (with same $\lambda$ and $D$ ) the separation between the slits needs to be changed to
(a) 1.7 mm (b) 1.8 mm (c) 2.1 mm (d) 1.9 mm

Answer

(d) 1.9 mm

Angular fringe width $\theta = \lambda/d$ , so $d \propto 1/\theta$ for fixed $\lambda$ . $d_2 = 2\ \text{mm} \times \dfrac{0.20}{0.21} \approx 1.9$ mm. A wider angle needs closer slits.

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2018 · NEET-UG (India) · 4 marks

An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of
(a) small focal length and small diameter (b) small focal length and large diameter (c) large focal length and large diameter (d) large focal length and small diameter

Answer

(c) large focal length and large diameter

Angular magnification of a telescope is $m = f_o/f_e$ , so a large $f_o$ is needed. Resolving power is proportional to the aperture $D$ (limit $1.22\lambda/D$ ), so a large diameter is needed too.

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2019 · NEET-UG (India) · 4 marks

In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away was found to be $0.2^\circ$ . What will be the angular width of the first minima if the entire experimental apparatus is immersed in water? ( $\mu_{water}=4/3$ )
(a) $0.266^\circ$ (b) $0.15^\circ$ (c) $0.05^\circ$ (d) $0.1^\circ$

Answer

(b) $0.15^\circ$

Angular width $\theta \propto \lambda$ , and in a medium $\lambda' = \lambda/\mu$ . $\theta' = 0.2^\circ \times \dfrac34 = 0.15^\circ$ .

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2019 · NEET-UG (India) · 4 marks

Which colour of light has the longest wavelength?
(a) Red (b) Blue (c) Green (d) Violet

Answer

(a) Red

In the visible spectrum red has the longest wavelength (about 700 nm) and violet the shortest (about 400 nm). So the order of wavelength is red > green > blue > violet.

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2019 · NEET-UG (India) · 4 marks

Two similar thin equi-convex lenses, of focal length $f$ each, are kept coaxially in contact with each other such that the focal length of the combination is $F_1$ . When the space between the two lenses is filled with glycerin (which has the same refractive index ( $\mu=1.5$ ) as that of glass) then the equivalent focal length is $F_2$ . The ratio $F_1:F_2$ will be
(a) $2:1$ (b) $1:2$ (c) $2:3$ (d) $3:4$

Answer

(b) $1:2$

In contact, $1/F_1 = 2/f$ , so $F_1 = f/2$ . Glycerin has the same index as glass, so the filled combination acts as a single equi-convex lens with the same two curved surfaces: $1/F_2 = (1.5-1)(2/R) = 1/f$ , so $F_2 = f$ . Hence $F_1:F_2 = 1:2$ .

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2019 · NEET-UG (India) · 4 marks

Pick the wrong answer in the context of rainbow.
(a) When the light rays undergo two internal reflections in a water drop, a secondary rainbow is formed (b) The order of colours is reversed in the secondary rainbow (c) An observer can see a rainbow when his front is towards the sun (d) Rainbow is a combined effect of dispersion, refraction and reflection of sunlight

Answer

(c) An observer can see a rainbow when his front is towards the sun

A rainbow is seen only when the sun is behind the observer, since light is dispersed and reflected back toward the eye at about $42^\circ$ from the antisolar point. So (c) is the wrong statement. In the secondary bow, two internal reflections reverse the colour order, and the whole effect is dispersion, refraction and reflection.

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2019 · NEET-UG (India) · 4 marks

In total internal reflection, when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?
(a) $180^\circ$ (b) $0^\circ$ (c) Equal to angle of incidence (d) $90^\circ$

Answer

(d) $90^\circ$

At the critical angle, the refracted ray grazes the interface, so the angle of refraction is $90^\circ$ (from $\sin C=\dfrac{1}{\mu}$ with $\sin r=1$ ). Beyond $C$ there is no refracted ray and total internal reflection occurs.

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2020 · NEET-UG (India) · 4 marks

The Brewster's angle $i_b$ for an interface should be
(a) $45^\circ<i_b<90^\circ$ (b) $i_b=90^\circ$ (c) $0^\circ<i_b<30^\circ$ (d) $30^\circ<i_b<45^\circ$

Answer

(a) $45^\circ<i_b<90^\circ$

Brewster's law: $\tan i_b=\mu$ . Since $\mu>1$ for an interface from air to a denser medium, $\tan i_b>1$ . Hence $45^\circ<i_b<90^\circ$ ; $i_b=90^\circ$ would need infinite $\mu$ .

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2020 · NEET-UG (India) · 4 marks

A ray is incident at an angle of incidence $i$ on one surface of a small angle prism (with angle of prism $A$ ) and emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$ , then the angle of incidence is nearly equal to
(a) $\mu A$ (b) $\dfrac{\mu A}{2}$ (c) $\dfrac{A}{2\mu}$ (d) $\dfrac{2A}{\mu}$

Answer

(a) $\mu A$

Normal emergence means the internal angle at the second face is zero, so the internal angle at the first face is $r_1=A$ . Snell's law for small angles: $i=\mu r_1=\mu A$ .

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2020 · NEET-UG (India) · 4 marks

Assume that light of wavelength 600 nm is coming from a star. The limit of resolution of a telescope whose objective has a diameter of 2 m is
(a) $7.32\times10^{-7}$ rad (b) $6.00\times10^{-7}$ rad (c) $3.66\times10^{-7}$ rad (d) $1.83\times10^{-7}$ rad

Answer

(c) $3.66\times10^{-7}$ rad

Limit of resolution: $\Delta\theta=\dfrac{1.22\lambda}{D}=\dfrac{1.22\times600\times10^{-9}}{2}=3.66\times10^{-7}$ rad. Omitting the factor 1.22 gives $3.0\times10^{-7}$ , and forgetting the division by $D$ gives a much larger value.

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2020 · NEET-UG (India) · 4 marks

In a guitar, two strings $A$ and $B$ made of the same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in $B$ is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of $A$ is 530 Hz, the original frequency of $B$ will be
(a) 536 Hz (b) 537 Hz (c) 523 Hz (d) 524 Hz

Answer

(d) 524 Hz

Beat frequency is $|f_A - f_B| = 6$ Hz, so $f_B = 530 \pm 6$ , i.e. 524 Hz or 536 Hz. Frequency of a string goes as $f \propto \sqrt{T}$ , so decreasing the tension of $B$ lowers $f_B$ .

If $f_B$ were 536 Hz, lowering it would bring it closer to 530 Hz and the beats would fall below 6 Hz, which contradicts the rise to 7 Hz. With $f_B = 524$ Hz, lowering it moves it further from $f_A$ , giving $530 - 523 = 7$ Hz. So the original frequency is 524 Hz (this matches NTA's key).

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2021 · NEET-UG (India) · 4 marks

A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since:
(a) A large aperture contributes to the quality and visibility of the images (b) A large area of the objective ensures better light gathering power (c) A large aperture provides a better resolution (d) All of the above

Answer

(d) All of the above

A large aperture collects more light (better light gathering and brighter, more visible images) and gives better resolving power ( $\propto D/\lambda$ ). A large focal length of the objective also gives higher magnification $f_o/f_e$ . All the stated reasons hold, so (d) is correct.

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2021 · NEET-UG (India) · 4 marks

A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm will be:
(a) 50 (b) 30 (c) 25 (d) 15

Answer

(d) 15

For a parallel beam to remain parallel, the lens pair acts as a telescope in normal adjustment: the second focal point of the convex lens must coincide with the focal point of the concave lens. So $d=f_A-|f_B|=20-5=15$ cm. The sum, 25 cm, would apply to two convex lenses.

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2021 · NEET-UG (India) · 4 marks

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of:
(a) 30 cm from the plane mirror, it would be a virtual image. (b) 20 cm from the plane mirror, it would be a virtual image. (c) 20 cm from the lens, it would be a real image. (d) 30 cm from the lens, it would be a real image.

Answer

(c) 20 cm from the lens, it would be a real image.

The lens ( $u=-60$ , $f=30$ ) forms an image at $v=60$ cm from the lens, which is 20 cm behind the mirror at 40 cm. The mirror treats this as a virtual object and forms a real image 20 cm in front of the mirror, which is 20 cm from the lens. This matches the answer key's option (c).

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2022 · NEET-UG (India) · 4 marks

In a Young's double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same region of the screen is:
(a) 6 (b) 8 (c) 9 (d) 12

Answer

(d) 12

Fringe width $\beta = \lambda D/d$ , so the number of fringes in a fixed region is $\propto 1/\lambda$ . Hence $N_2 = 8\times\dfrac{600}{400} = 12$ .

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2022 · NEET-UG (India) · 4 marks

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:
(a) 1 : 1 (b) $\sqrt{2} : 1$ (c) $1 : \sqrt{2}$ (d) 1 : 2

Answer

(c) $1 : \sqrt{2}$

Wave speed on a string is $v = \sqrt{T/\mu}$ , so $v\propto\sqrt{T}$ . Doubling the tension gives $v_f = \sqrt2\,v_i$ , so $v_i : v_f = 1:\sqrt2$ .

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2022 · NEET-UG (India) · 4 marks

A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is:
(a) +2 D (b) +20 D (c) +5 D (d) Infinity

Answer

(c) +5 D

Lensmaker formula: $\dfrac1f = (n-1)\left(\dfrac1{R_1}-\dfrac1{R_2}\right) = 0.5\left(\dfrac1{20}+\dfrac1{20}\right) = \dfrac1{20}$ cm $^{-1}$ . So $f = 20$ cm $= 0.2$ m and $P = 1/f = +5$ D.

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2022 · NEET-UG (India) · 4 marks

A light ray falls on a glass surface of refractive index $\sqrt{3}$ , at an angle $60^\circ$ . The angle between the refracted and reflected rays would be:
(a) $30^\circ$ (b) $60^\circ$ (c) $90^\circ$ (d) $120^\circ$

Answer

(c) $90^\circ$

$\tan i_p = \mu = \sqrt3$ gives $i_p = 60^\circ$ , so the incidence is at the Brewster angle. Then the reflected and refracted rays are perpendicular. Check: $\sin60^\circ/\sin r=\sqrt3$ gives $r=30^\circ$ , and the angle between the rays is $180^\circ-60^\circ-30^\circ=90^\circ$ .

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2022 · NEET-UG (India) · 4 marks

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are $1.5 \times 10^8$ m/s and $2.0 \times 10^8$ m/s, respectively. The critical angle for a ray of light for these two media is:
(a) $\sin^{-1}(0.500)$ (b) $\sin^{-1}(0.750)$ (c) $\tan^{-1}(0.500)$ (d) $\tan^{-1}(0.750)$

Answer

(b) $\sin^{-1}(0.750)$

Refractive index is inversely proportional to speed, so A is denser (slower). Total internal reflection occurs going from A to B with $\sin C = \dfrac{n_B}{n_A} = \dfrac{v_A}{v_B} = \dfrac{1.5\times10^8}{2.0\times10^8} = 0.75$ .

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2023 · NEET-UG (India) · 4 marks

Light travels a distance $x$ in time $t_1$ in air and $10x$ in time $t_2$ in another denser medium. What is the critical angle for this medium?
(a) $\sin^{-1}\left(\frac{t_2}{t_1}\right)$ (b) $\sin^{-1}\left(\frac{10t_2}{t_1}\right)$ (c) $\sin^{-1}\left(\frac{t_1}{10t_2}\right)$ (d) $\sin^{-1}\left(\frac{10t_1}{t_2}\right)$

Answer

(d) $\sin^{-1}\left(\dfrac{10t_1}{t_2}\right)$

Speed in air $c = x/t_1$ , speed in the medium $v = 10x/t_2$ . So $n = c/v = \dfrac{t_2}{10t_1}$ and $\sin C = \dfrac1n = \dfrac{10t_1}{t_2}$ .

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2023 · NEET-UG (India) · 4 marks

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:
(a) 1 : 2 (b) 2 : 1 (c) 1 : 3 (d) 3 : 1

Answer

(b) 2 : 1

An open pipe of length $L$ has fundamental $f_o = \frac{v}{2L}$ , while a closed pipe has $f_c=\frac{v}{4L}$ . Hence $f_o : f_c = 2:1$ .

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2023 · NEET-UG (India) · 4 marks

For Young's double slit experiment, two statements are given below:
Statement I: If screen is moved away from the plane of slits, angular separation of the fringes remains constant. Statement II: If the monochromatic source is replaced by another monochromatic source of larger wavelength, the angular separation of fringes decreases.
In the light of the above statements, choose the correct answer from the options given below:
(a) Both Statement I and Statement II are true. (b) Both Statement I and Statement II are false. (c) Statement I is true but Statement II is false. (d) Statement I is false but Statement II is true.

Answer

(c) Statement I is true but Statement II is false.

Angular fringe separation is $\theta=\frac{\lambda}{d}$ , which does not depend on the screen distance $D$ , so Statement I is true. Increasing $\lambda$ increases $\theta$ , so Statement II (decreases) is false.

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2023 · NEET-UG (India) · 4 marks

Two thin lenses are of same focal lengths ( $f$ ), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be:
(a) Zero (b) $\frac{f}{4}$ (c) $\frac{f}{2}$ (d) Infinite

Answer

(d) Infinite

$\frac1F=\frac1f+\frac{1}{-f}=0$ , so $F=\infty$ . The combination acts like a plane glass plate with zero net power.

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2024 · NEET-UG (India) · 4 marks

If the monochromatic source in Young's double slit experiment is replaced by white light, then:
(a) There will be a central dark fringe surrounded by a few coloured fringes (b) There will be a central bright fringe surrounded by a few coloured fringes. (c) All bright fringes will be of equal width (d) Interference pattern will disappear.

Answer

(b) There will be a central bright fringe surrounded by a few coloured fringes.

At the centre the path difference is zero for every colour, so all colours form a bright (white) fringe. Away from it the different fringe widths $\beta=\frac{\lambda D}{d}$ separate the colours, giving a few coloured fringes before the pattern washes out. A central dark fringe is wrong, as is equal fringe width.

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2024 · NEET-UG (India) · 4 marks

An unpolarized light beam strikes a glass surface at Brewster's angle. Then:
(a) The refracted light will be completely polarised (b) Both the reflected and refracted light will be completely polarised (c) The reflected light will be completely polarized but the refracted light will be partially polarized (d) The reflected light will be partially polarized.

Answer

(c) The reflected light will be completely polarized but the refracted light will be partially polarized

At Brewster's angle the reflected ray is fully plane polarised (perpendicular to the plane of incidence). The refracted ray contains the rest of the perpendicular component and all the parallel component, so it is only partially polarised.

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2024 · NEET-UG (India) · 4 marks

A small telescope has an objective of focal length 140 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object is:
(a) 28 (b) 17 (c) 32 (d) 34

Answer

(a) 28

For a telescope in normal adjustment viewing a distant object, $m=\frac{f_o}{f_e}$ . $m=\frac{140}{5}=28$ . Option (d) 34 would come from wrongly adding the focal lengths or using the near-point formula.

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2025 · NEET-UG (India) · 4 marks

The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at $22.5^\circ$ from the polarization axis of one of the polaroid, is ( $I_0$ is the intensity of polarized light after passing through the first polaroid):
(a) $\frac{I_0}{8}$ (b) $\frac{I_0}{16}$ (c) $\frac{I_0}{2}$ (d) $\frac{I_0}{4}$

Answer

(a) $\frac{I_0}{8}$

The middle polaroid is $22.5^\circ$ from the first axis and so $67.5^\circ$ from the crossed one. By Malus' law: $I=I_0\cos^2 22.5^\circ\cos^2 67.5^\circ=I_0\cos^2 22.5^\circ\sin^2 22.5^\circ$ . This equals $I_0\left(\frac{\sin45^\circ}{2}\right)^2=\frac{I_0}{8}$ . Option (d) $\frac{I_0}{4}$ is not reached at this angle: even the best angle, $45^\circ$ , gives only $\frac{I_0}{4}$ .

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2025 · NEET-UG (India) · 4 marks

A microscope has an objective of focal length 2 cm, eyepiece of focal length 4 cm and the tube length of 40 cm. If the distance of distinct vision of eye is 25 cm, the magnification in the microscope is:
(a) 150 (b) 250 (c) 100 (d) 125

Answer

(d) 125

Using the standard approximation for a compound microscope with the tube length $L$ taken as the separation of the lenses and the final image at the near point: $m\approx\frac{L}{f_o}\cdot\frac{D}{f_e}$ . $m=\frac{40}{2}\times\frac{25}{4}=20\times6.25=125$ .

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2025 · NEET-UG (India) · 4 marks

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:
(a) $\frac{3f}{2}$ (b) $2f$ (c) $\frac{f}{2}$ (d) $f$

Answer

(d) $f$

The open pipe of length $L$ has $f=\frac{v}{2L}$ . Dipped to half its length, it becomes a closed pipe of length $\frac L2$ , with fundamental $f_{new}=\frac{v}{4(L/2)}=\frac{v}{2L}=f$ . The frequency is unchanged.

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2025 · NEET-UG (India) · 4 marks

In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power ( $p$ ) and magnification ( $m$ ) for each lens will be, respectively:
(a) $4p$ and $m^4$ (b) $p^4$ and $m^4$ (c) $4p$ and $4m$ (d) $p^4$ and $4m$

Answer

(a) $4p$ and $m^4$

Powers of thin lenses in contact add, so $P=p+p+p+p=4p$ . For lenses in series the image of one is the object of the next, so the magnifications multiply: $m_{tot}=m\cdot m\cdot m\cdot m=m^4$ . Options (c) and (d) wrongly add magnifications.

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2025 · NEET-UG (India) · 4 marks

An unpolarized light beam travelling in air is incident on a medium of refractive index 1.73 at Brewster's angle. Then:
(a) Both reflected and transmitted light are perfectly polarized with angles of reflection and refraction close to $60^\circ$ and $30^\circ$ , respectively (b) Transmitted light is completely polarized with angle of refraction close to $30^\circ$ (c) Reflected light is completely polarized and the angle of reflection is close to $60^\circ$ (d) Reflected light is partially polarized and the angle of reflection is close to $30^\circ$

Answer

(c) Reflected light is completely polarized and the angle of reflection is close to $60^\circ$

At Brewster's angle $\tan\theta_B=\mu=1.73\approx\sqrt3$ , so $\theta_B\approx60^\circ$ . The reflected ray is then completely plane polarized, perpendicular to the refracted ray. The refracted ray is at $30^\circ$ but is only partially polarized, which rules out (a) and (b). Option (d) is wrong because the reflected light is fully, not partially, polarized.

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Past questions and answers

5.For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be: (a) 5 cm (b) 2.5 cm (c) 1.67 cm (d) 1.5 cm

8.If focal length of objective lens is increased then magnifying power of: (a) microscope and telescope both will increase. (b) microscope and telescope both will decrease. (c) microscope will decrease but that of telescope will increase. (d) microscope will increase but that of telescope decrease.

10.The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are: (velocity of sound =340 m s−1=340\ \mathrm{m\,s^{-1}}=340 ms−1) (a) 5 (b) 7 (c) 6 (d) 4

14.A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is: (a) 10.5 Hz (b) 105 Hz (c) 155 Hz (d) 205 Hz

21.An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance: (a) 54.0 cm (b) 37.3 cm (c) 46.0 cm (d) 50.0 cm

23.An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is: (a) 200 cm (b) 66.7 cm (c) 100 cm (d) 150 cm

25.Young's double slit experiment is first performed in air and then in a medium other than air. It is found that the 8th bright fringe in the medium lies where the 5th dark fringe lies in air. The refractive index of the medium is nearly (a) 1.59 (b) 1.69 (c) 1.78 (d) 1.25

27.The ratio of resolving powers of an optical microscope for two wavelengths λ1=4000\lambda_1=4000λ1​=4000 Å and λ2=6000\lambda_2=6000λ2​=6000 Å is (a) 9:49:49:4 (b) 3:23:23:2 (c) 16:8116:8116:81 (d) 8:278:278:27

29.The two nearest harmonics of a tube closed at one end and open at the other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system? (a) 20 Hz (b) 30 Hz (c) 40 Hz (d) 10 Hz

35.The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is (a) 16 cm (b) 13.2 cm (c) 12.5 cm (d) 8 cm

40.Which colour of light has the longest wavelength? (a) Red (b) Blue (c) Green (d) Violet

43.In total internal reflection, when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction? (a) 180∘180^\circ180∘ (b) 0∘0^\circ0∘ (c) Equal to angle of incidence (d) 90∘90^\circ90∘

44.The Brewster's angle ibi_bib​ for an interface should be (a) 45∘<ib<90∘45^\circ<i_b<90^\circ45∘<ib​<90∘ (b) ib=90∘i_b=90^\circib​=90∘ (c) 0∘<ib<30∘0^\circ<i_b<30^\circ0∘<ib​<30∘ (d) 30∘<ib<45∘30^\circ<i_b<45^\circ30∘<ib​<45∘

49.A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm will be: (a) 50 (b) 30 (c) 25 (d) 15

52.If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is: (a) 1 : 1 (b) 2:1\sqrt{2} : 12​:1 (c) 1:21 : \sqrt{2}1:2​ (d) 1 : 2

53.A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is: (a) +2 D (b) +20 D (c) +5 D (d) Infinity

54.A light ray falls on a glass surface of refractive index 3\sqrt{3}3​, at an angle 60∘60^\circ60∘. The angle between the refracted and reflected rays would be: (a) 30∘30^\circ30∘ (b) 60∘60^\circ60∘ (c) 90∘90^\circ90∘ (d) 120∘120^\circ120∘

57.The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is: (a) 1 : 2 (b) 2 : 1 (c) 1 : 3 (d) 3 : 1

59.Two thin lenses are of same focal lengths (fff), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be: (a) Zero (b) f4\frac{f}{4}4f​ (c) f2\frac{f}{2}2f​ (d) Infinite

62.A small telescope has an objective of focal length 140 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object is: (a) 28 (b) 17 (c) 32 (d) 34

64.A microscope has an objective of focal length 2 cm, eyepiece of focal length 4 cm and the tube length of 40 cm. If the distance of distinct vision of eye is 25 cm, the magnification in the microscope is: (a) 150 (b) 250 (c) 100 (d) 125

65.A pipe open at both ends has a fundamental frequency fff in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to: (a) 3f2\frac{3f}{2}23f​ (b) 2f2f2f (c) f2\frac{f}{2}2f​ (d) fff

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:
(a) 5 cm (b) 2.5 cm (c) 1.67 cm (d) 1.5 cm

If focal length of objective lens is increased then magnifying power of:
(a) microscope and telescope both will increase. (b) microscope and telescope both will decrease. (c) microscope will decrease but that of telescope will increase. (d) microscope will increase but that of telescope decrease.

The number of possible natural oscillations of air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz are: (velocity of sound $=340\ \mathrm{m\,s^{-1}}$ )
(a) 5 (b) 7 (c) 6 (d) 4

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:
(a) 10.5 Hz (b) 105 Hz (c) 155 Hz (d) 205 Hz

An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance:
(a) 54.0 cm (b) 37.3 cm (c) 46.0 cm (d) 50.0 cm

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is:
(a) 200 cm (b) 66.7 cm (c) 100 cm (d) 150 cm

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that the 8th bright fringe in the medium lies where the 5th dark fringe lies in air. The refractive index of the medium is nearly
(a) 1.59 (b) 1.69 (c) 1.78 (d) 1.25

The ratio of resolving powers of an optical microscope for two wavelengths $\lambda_1=4000$ Å and $\lambda_2=6000$ Å is
(a) $9:4$ (b) $3:2$ (c) $16:81$ (d) $8:27$

The two nearest harmonics of a tube closed at one end and open at the other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?
(a) 20 Hz (b) 30 Hz (c) 40 Hz (d) 10 Hz

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is
(a) 16 cm (b) 13.2 cm (c) 12.5 cm (d) 8 cm

Which colour of light has the longest wavelength?
(a) Red (b) Blue (c) Green (d) Violet

In total internal reflection, when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?
(a) $180^\circ$ (b) $0^\circ$ (c) Equal to angle of incidence (d) $90^\circ$

The Brewster's angle $i_b$ for an interface should be
(a) $45^\circ<i_b<90^\circ$ (b) $i_b=90^\circ$ (c) $0^\circ<i_b<30^\circ$ (d) $30^\circ<i_b<45^\circ$

A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm will be:
(a) 50 (b) 30 (c) 25 (d) 15

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:
(a) 1 : 1 (b) $\sqrt{2} : 1$ (c) $1 : \sqrt{2}$ (d) 1 : 2

A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is:
(a) +2 D (b) +20 D (c) +5 D (d) Infinity

A light ray falls on a glass surface of refractive index $\sqrt{3}$ , at an angle $60^\circ$ . The angle between the refracted and reflected rays would be:
(a) $30^\circ$ (b) $60^\circ$ (c) $90^\circ$ (d) $120^\circ$

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:
(a) 1 : 2 (b) 2 : 1 (c) 1 : 3 (d) 3 : 1

Two thin lenses are of same focal lengths ( $f$ ), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be:
(a) Zero (b) $\frac{f}{4}$ (c) $\frac{f}{2}$ (d) Infinite

A small telescope has an objective of focal length 140 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object is:
(a) 28 (b) 17 (c) 32 (d) 34

A microscope has an objective of focal length 2 cm, eyepiece of focal length 4 cm and the tube length of 40 cm. If the distance of distinct vision of eye is 25 cm, the magnification in the microscope is:
(a) 150 (b) 250 (c) 100 (d) 125

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:
(a) $\frac{3f}{2}$ (b) $2f$ (c) $\frac{f}{2}$ (d) $f$