Wave Optics · JEE Main previous year questions

In the Young's double slit experiment, the distance between the slits varies in time as $d(t)=d_0+a_0\sin \omega t$; where $d_0$, $\omega$ and $a_0$ are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as :

1. A.$\frac{2\lambda D(d_0)}{(d_0^2-a_0^2)}$
2. B.$\frac{2\lambda D{a}_0}{(d_0^2-a_0^2)}$
3. C.$\frac{\lambda D}{d_0^2}{a}_0$
4. D.$\frac{\lambda D}{d_0+a_0}$

A linearly polarized electromagnetic wave in vacuum $$E=3.1\cos \left[(1.8)z-(5.4\times 10^6)t\right]\hat{i}N/C$$ is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

1. A.The wavelength is 5.4 m
2. B.The frequency of electromagnetic wave is $54\times 10^4$ Hz.
3. C.The transmitted wave will be $3.1\cos \left[(1.8)z-(5.4\times 10^6)t\right]\hat{i}N/C$
4. D.The reflected wave will be $3.1\cos \left[(1.8)z+(5.4\times 10^6)t\right]\hat{i}N/C$

In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of $5890\text{ A˚}$ is :-

1. A.$1178\times 10^{-9}\text{ m}$
2. B.$1178\times 10^{-6}\text{ m}$
3. C.$1178\times 10^{-12}\text{ m}$
4. D.$5890\times 10^{-7}\text{ m}$

A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is 'x' nm. The value of 'x' to the nearest integer is ____________.

In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed one meter away. When a light of wavelength 500 nm is used, the fringe separation will be :

1. A.0.50 mm
2. B.0.25 mm
3. C.1 mm
4. D.0.75 mm

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter $0.1\mu \mathrm{m}$. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that:

1. A.its size increases, but intensity decreases
2. B.its size increases, and intensity increases
3. C.its size decreases, but intensity increases
4. D.its sizes decreases, and intensity decreases

In a Young's double slit experiment, light of 500 nm is used to produce an interference pattern. When the distance between the slits is 0.05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to

1. A.$0.17^{\circ }$
2. B.$1.7^{\circ }$
3. C.$0.57^{\circ }$
4. D.$0.07^{\circ }$

Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light source ($\lambda =632.8\text{ nm}$). The distance between the screen and the slits is 100 cm. If a bright fringe is observed on a screen at a distance of 1.27 mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close is

1. A.$1.27\mu \mathrm{m}$
2. B.$2.05\mu \mathrm{m}$
3. C.2.87 nm
4. D.2 nm

In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of a wavelength 700 nm is used. If the wavelength of light is changed to 400 nm, the number of fringes observed in the same segment of the screen would be

1. A.28
2. B.24
3. C.30
4. D.18

In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes are observed on the same section of the screen when another light source of wavelength $\lambda$ is used. Then the value of $\lambda$ is (in nm) _______.

In a double slit experiment, at a certain point on the screen the path difference between the two interfering waves is $\frac{1}{8}\text{th}$ of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :

1. A.0.853
2. B.0.568
3. C.0.672
4. D.0.760

A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just 10% of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is :

1. A.$71.6^{\circ }$
2. B.$90^{\circ }$
3. C.$18.4^{\circ }$
4. D.$45^{\circ }$

Visible light of wavelength $6000\times 10^{-8}\mathrm{cm}$ falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at $60^{\circ }$ from the central maximum. If the first minimum is produced at ${\theta }_1$, then ${\theta }_1$, is close to :

1. A.$45^{\circ }$
2. B.$30^{\circ }$
3. C.$25^{\circ }$
4. D.$20^{\circ }$

In a Young's double slit experiment, the separation between the slits is 0.15 mm. in the experiment, a source of light of wavelengh 589 nm is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the screen is :

1. A.4.9 mm
2. B.5.9 mm
3. C.6.9 mm
4. D.3.9 mm

In a double slit experiment, when a thin film of thickness t having refractive index $\mu$ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is ($\lambda$ is the wavelength of the light used) :

1. A.$\frac{\lambda }{2(\mu -1)}$
2. B.$\frac{\lambda }{(2\mu -1)}$
3. C.$\frac{2\lambda }{(\mu -1)}$
4. D.$\frac{\lambda }{(\mu -1)}$

A system of three polarizers $P_1,P_2,P_3$ is set up such that the pass axis of $P_3$ is crossed with respect to that of $P_1$. The pass axis of $P_2$ is inclined at $60^{\circ }$ to the pass axis of $P_3$. When a beam of unpolarized light of intensity $I_0$ is incident on $P_1$, the intensity of light transmitted by the three polarizers is I. The ratio $\left(\frac{I_0}{I}\right)$ equals (nearly) :

1. A.10.67
2. B.5.33
3. C.16.00
4. D.1.80

In a Young's double slit experiment, the ratio of the slit's width is 4 : 1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be :

1. A.25 : 9
2. B.4 : 1
3. C.$(\sqrt{3}+1{)}^4:16$
4. D.9 : 1

The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index $\mu$ is put in front of one of the slits, the central maximum gets shifted by a distance equal to n fringe widths. If the wavelength of light used is $\lambda$, t will be : [Figure: slits separated by a, screen at distance D]

1. A.$\frac{D\lambda }{a(\mu -1)}$
2. B.$\frac{2nD\lambda }{a(\mu -1)}$
3. C.$\frac{2D\lambda }{a(\mu -1)}$
4. D.$\frac{n\lambda }{(\mu -1)}$

In a double-slit experiment, green light ($5303\text{ A˚}$) falls on a double slit having a separation of $19.44\mu \mathrm{m}$ and a width of $4.05\mu \mathrm{m}$. The number of bright fringes between the first and the second diffraction minima is :

1. A.04
2. B.05
3. C.10
4. D.09

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio :

1. A.16 : 9
2. B.25 : 9
3. C.4 : 1
4. D.5 : 3

1. A.$\sqrt{\frac{5}{3}}$
2. B.$\frac{3}{\sqrt{5}}$
3. C.$\frac{5}{\sqrt{3}}$
4. D.$\frac{4}{3}$

Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B, the intensity of emergent light is reduced to I/3. The angle between the polarizers A and C is $\theta$. Then :

1. A.$\cos \theta ={\left(\frac{2}{3}\right)}^{1/2}$
2. B.$\cos \theta ={\left(\frac{2}{3}\right)}^{1/4}$
3. C.$\cos \theta ={\left(\frac{1}{3}\right)}^{1/2}$
4. D.$\cos \theta ={\left(\frac{1}{3}\right)}^{1/4}$

The angular width of the central maximum in a single slit diffraction pattern is $60^{\circ }$. The width of the slit is $1\mu \text{m}$. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)

1. A.$100\mu \text{m}$
2. B.$25\mu \text{m}$
3. C.$50\mu \text{m}$
4. D.$75\mu \text{m}$

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is :

1. A.$60^{\circ }$
2. B.$30^{\circ }$
3. C.$45^{\circ }$
4. D.$0^{\circ }$

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength $6000\mathring{\mathrm{A}}$ and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is :

1. A.$3\mathrm{mm}$
2. B.$9\mathrm{mm}$
3. C.$4.5\mathrm{mm}$
4. D.$1.5\mathrm{mm}$