Wave Optics — JEE Main PYQs

In a Young's double slit experiment, the intensity at some point on the screen is found to be $\frac{3}{4}$ times of the maximum of the interference pattern. The path difference between the interfering waves at this point is $\frac{\lambda}{x}$ where $\lambda$ is wavelength of the incident light. The value of $x$ is ________.

A slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between $1^{\text{st}}$ and $3^{\text{rd}}$ minima in the diffraction pattern produced on a screen placed at a distance $D$ from the slit system is _________.

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5 \times 10^{-7}$ radian. The value of $R$ is _________ cm.

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

[Figure: Incident light rays striking the horizontal air-medium interface; coordinate axes shown with $x$ and $y$ along the interface plane and $z$ pointing downward into the medium]

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at $30°$ and $90°$, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at $60°$ with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ________.

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index $1.56$, the central fringe shifts to the position of $7^{\text{th}}$ bright fringe, obtained with both slits uncovered. If the light source wavelength is $450 \text{ nm}$, the thickness of mica sheet is $\alpha \times 10^{-9} \text{ m}$. The value of $\alpha$ is __________.

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4 \text{ } \mu\text{m}$. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be ____ $\mu$m.

The maximum intensity in a Young's double slit experiment is $I_0$. Distance between the slits ($d$) is $5\lambda$, where $\lambda$ is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at $D = 10d$ is __________.

In interference experiment the path difference between two interfering waves at a point $A$ on the screen is $\lambda/3$, where $\lambda$ is the wavelength of these waves, and at another point $B$ the path difference is $\lambda/6$. The ratio of intensities at points $A$ and $B$ is ________.

An unpolarized light of intensity $I_o$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is $0°$ and intensity of light emerged from analyser is $\frac{3}{8} I_o$, the angle of rotation of the light by the solution with respect to analyser is ______ degrees.

In a Young double slit experiment, the wavelength of incident light is 6000 Å, the separation between slits $S_1$ and $S_2$ is 5 cm and the distance between slits plane and screen is 50 cm, as shown in the figure below. If the resultant intensity at $P$ is equal to the intensity due to individual slits, the path difference between interfering waves is __________ Å.

[Figure: Young's double slit arrangement — source S ($\lambda = 6000$ Å) illuminating slits $S_1$ and $S_2$; screen at 50 cm from the slit plane with central point $O'$ and an off-axis point $P$ below it.]

Some distant star is to be observed by some telescope of diameter of objective lens $a$, at an angular resolution of $3.0 \times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is $500\,\text{nm}$, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

A light wave is propagating with plane wave fronts of the type $x+y+z=\text{constant}$. The angle made by the direction of wave propagation with the $x$-axis is :

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is $30°$ in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is _________ $\mu\mathrm{m}$.

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $x$I. The value of $x$ is __________.

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is :

Two polarisers $\mathrm{P_1}$ and $\mathrm{P_2}$ are placed in such a way that the intensity of the transmitted light will be zero. A third polariser $\mathrm{P_3}$ is inserted in between $\mathrm{P_1}$ and $\mathrm{P_2}$, at particular angle between $\mathrm{P_2}$ and $\mathrm{P_3}$. The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers $\mathrm{P_2}$ and $\mathrm{P_3}$ is :

In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the 20 maxima of the double slit pattern are contained within the central maximum of the single slit diffraction pattern, then the width of each slit is $x \times 10^{-3}$ cm, where $x$-value is ______.

Two plane polarized light waves combine at a certain point whose electric field components are

$$E_1 = E_0\ \mathrm{Sin}\ \omega t$$

$$E_2 = E_0\ \mathrm{Sin}\left(\omega t + \frac{\pi}{3}\right)$$

Find the amplitude of the resultant wave.

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.

Reason (R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.

In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light.

Reason (R) : The fringe width is directly proportional to the wavelength of light.

In the light of the above statements, choose the correct answer from the options given below :

The width of one of the two slits in Young's double slit experiment is $d$ while that of the other slit is $xd$. If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is $9 : 4$ then what is the value of $x$ ?

(Assume that the field strength varies according to the slit width.)

The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is

Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm. The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm. The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m, will be :

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $\mathrm{P}_1$ and $\mathrm{P}_2$ are orthogonal to each other. The polarizer $\mathrm{P}_3$, whose transmission axis is at $45°$ to the transmission axes of $\mathrm{P}_1$ and $\mathrm{P}_2$, covers both the slits. An unpolarized light of wavelength $\lambda$ and intensity $\mathrm{I}_0$ is incident on $\mathrm{P}_1$ and $\mathrm{P}_2$. At a point after $\mathrm{P}_3$, where the path difference between the light waves from $s_1$ and $s_2$ is $\frac{\lambda}{3}$, the intensity is :

[Figure: unpolarized light of wavelength λ and intensity I₀ is incident on polarizers P₁ and P₂ placed over slits s₁ and s₂ respectively; polarizer P₃ placed after them covers both slits]

A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with 10th bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same 10th bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be _____ mm.

A thin transparent film with refractive index 1.4, is held on circular ring of radius 1.8 cm. The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is __________ $\pi \times 10^{-13}\,\mathrm{m^3/s}$.

Two wavelengths $\lambda_1$ and $\lambda_2$ are used in Young's double slit experiment. $\lambda_1 = 450$ nm and $\lambda_2 = 650$ nm. The minimum order of fringe produced by $\lambda_2$ which overlaps with the fringe produced by $\lambda_1$ is n. The value of n is ________.

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:

Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is :

In Young's double slit experiment, carried out with light of wavelength 5000 Å, the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at $x = 0$ cm. The value of $x$ for third maxima is ________ mm.

In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be $x \times 10^{-5}$ m. The value of $x$ is :

Which of the following phenomena does not explain by wave nature of light.

A. reflection B. diffraction C. photoelectric effect D. interference E. polarization

Choose the most appropriate answer from the options given below:

Two coherent monochromatic light beams of intensities I and 4 I are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $x$ I. The value of $x$ is ________.

A parallel beam of monochromatic light of wavelength 600 nm passes through single slit of 0.4 mm width. Angular divergence corresponding to second order minima would be _______ $\times 10^{-3}$ rad.

Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is ________ $\times 10^{-4}$ m.

In a Young's double slit experiment, the intensity at a point is $\left(\dfrac{1}{4}\right)^{\text{th}}$ of the maximum intensity, the minimum distance of the point from the central maximum is ________ $\mu\mathrm{m}$.

(Given : $\lambda = 600$ nm, $d = 1.0$ mm, $D = 1.0$ m)

Monochromatic light of wavelength 500 nm is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index = 1.5), the central maximum is shifted to a position previously occupied by the $4^{th}$ bright fringe. The thickness of the glass-plate is ________ $\mu$m.

A monochromatic light of wavelength 6000$\text{Å}$ is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is :

A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm. The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit, will be :

In Young's double slit experiment, monochromatic light of wavelength 5000 Å is used. The slits are 1.0 mm apart and screen is placed at 1.0 m away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is ________ $\times 10^{-6}$ m.

In a double slit experiment shown in figure, when light of wavelength 400 nm is used, dark fringe is observed at $P$. If $D=0.2$ m, the minimum distance between the slits $S_1$ and $S_2$ is _______ mm.

[Figure: source on the left, slits $S_1$ and $S_2$ separated by distance $d$ on a vertical line; source is at distance $D$ from the slit plane and point $P$ is at distance $D$ on the other side, both on the line through $S_2$; dashed lines from source to $S_1$ and from $S_1$ to $P$ form a triangle]

The diffraction pattern of a light of wavelength 400 nm diffracting from a slit of width 0.2 mm is focused on the focal plane of a convex lens of focal length 100 cm. The width of the $1^{\text{st}}$ secondary maxima will be :

A beam of unpolarised light of intensity $I_o$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45°$ relative to that of $A$. The intensity of emergent light is:

Two waves of intensity ratio 1:9 cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $I_1$ (b) Waves are coherent is $I_2$ and differ in phase by $60°$. If $\frac{I_1}{I_2} = \frac{10}{x}$ then $x =$ ______.

When unpolarized light is incident at an angle of $60°$ on a transparent medium from air, the reflected ray is completely polarized. The angle of refraction in the medium is: