JEE Advanced Physics: Wave Optics PYQ Practice

Q 1 :

In a Young's double slit experiment, a combination of two glass wedges A and B, having refractive indices 1.7 and 1.5, respectively, are placed in front of the slits, as shown in the figure. The separation between the slits is $d$ = 2 mm and the shortest distance between the slits and the screen is D = 2 m. Thickness of the combination of the wedges is $t = 12 μ m$ . The value of $l$ as shown in the figure is 1 mm. Neglect any refraction effect at the slanted interface of the wedges. Due to the combination of the wedges, the central maximum shifts (in mm) with respect to O by ________. [2025]

[IMAGE 1172]

(1.2)

From figure, $x + y = 12 μ m$

$\frac{4}{12} = \frac{1}{x}$ $∴$ $x = 3 μ m, y = 9 μ m$

[IMAGE 1173]

$∴$ $Δ = - \frac{y d}{D} - (μ_{B} - 1) x - (μ_{A} - 1) y + (μ_{B} - 1) y + (μ_{A} - 1) x$

$- \frac{y d}{D} = - 0.5 \times 3 - 0.7 \times 9 + 0.5 \times 9 + 0.7 \times 3$

$- \frac{y d}{D} = - 0.5 \times 6 - 0.7 \times 6$ $\Rightarrow - \frac{y d}{D} = - 1.2 μ m$

$\Rightarrow y = \frac{1.2 \times D}{d} \times 10^{- 6}$

$= \frac{1.2 \times 2}{2 \times 10^{- 3}} \times 10^{- 6}$

$= 1.2 mm$

Q 2 :

A single slit diffraction experiment is performed to determine the slit width using the equation, $\frac{b d}{D} = m λ,$ where $b$ is the slit width, D the shortest distance between the slit and the screen, $d$ the distance between the $m^{t h}$ diffraction maximum and the central maximum, and $λ$ is the wavelength. D and $d$ are measured with scales of least count of 1 cm and 1 mm, respectively. The values of $λ$ and $m$ are known precisely to be 600 nm and 3, respectively. The absolute error (in $μ$ m) in the value of $b$ estimated using the diffraction maximum that occurs for m = 3 with $d$ = 5 mm and D = 1 m is ______. [2025]

(94.50)

Given, $\frac{b d}{D} = m λ$ $\Rightarrow b = \frac{D}{d} m λ$

$b = \frac{m λ D}{d} = \frac{3 \times 600 \times 10^{- 3} \times 1}{5 \times 10^{- 3}} μ m = 360 μ m$

$b_{\max} = \frac{3 \times 600 \times 10^{- 3} \times 1.01}{4 \times 10^{- 3}} μ m = 454.5 μ m$

Therefore, absolute error in $b$ ,

$= b_{\max} - b = 454.5 - 360 = 94.50 μ m$

Q 3 :

A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths $f_{e}$ and $f_{o}$ , respectively. Then [2006]

Column I Column II

(A) Intensity of light received by lens (p) Radius of aperture

(B) Angular magnification (q) Dispersion of lens

(C) Length of telescope (r) Focal length of objective lens and eyepiece lens

(D) Sharpness of image (s) Spherical aberration

(A) → (p); (B) → (r); (C) → (r); (D) → (p), (q), (r)
(A) → (p), (q), (r); (B) → (r); (C) → (r); (D) → (p)
(A) → (p), (q), (r); (B) → (p); (C) → (r); (D) → (r)
(A) → (p), (q), (r); (B) → (r); (C) → (p); (D) → (r)

1

2

3

4

(1)

(A) More the radius of aperture, more is the amount of light entering the telescope.

(B) Angular magnification, $M = \frac{f_{o}}{f_{e}}$

(C) Length of telescope, $L = f_{o} + f_{e}$

Sharpness of image depends on dispersion of lens, spherical aberration and radius of aperture.

Q 4 :

The figure shows a surface XY separating two transparent media, medium-1 and medium-2. The lines ab and cd represent wavefronts of a light wave travelling in medium-1 and incident on XY. The lines ef and gh represent wavefronts of the light wave in medium-2 after refraction. [2007]

[IMAGE 1174]

Q. Light travels as a

parallel beam in each medium
convergent beam in each medium
divergent beam in each medium
divergent beam in one medium and convergent beam in the other medium

1

2

3

4

(1)

For plane wavefronts, the beam of light is parallel. Hence, light travels as a parallel beam in each medium.

Q 5 :

The figure shows a surface XY separating two transparent media, medium-1 and medium-2. The lines ab and cd represent wavefronts of a light wave travelling in medium-1 and incident on XY. The lines ef and gh represent wavefronts of the light wave in medium-2 after refraction. [2007]

[IMAGE 1175]

Q. The phases of the light wave at $c, d, e$ and $f$ are $ϕ_{c}$ , $ϕ_{d}$ , $ϕ_{e}$ and $ϕ_{f}$ , respectively. It is given that $ϕ_{c} \neq ϕ_{f} .$

$ϕ_{c}$ cannot be equal to $ϕ_{d}$
$ϕ_{d}$ can be equal to $ϕ_{e}$
$(ϕ_{d} - ϕ_{f})$ is equal to $(ϕ_{c} - ϕ_{e})$
$(ϕ_{d} - ϕ_{c})$ is not equal to $(ϕ_{f} - ϕ_{e})$

1

2

3

4

(3)

Since points $c$ and $d$ are on the same wavefront,

$∴$ $ϕ_{d} = ϕ_{c}$

Similarly, $ϕ_{e} = ϕ_{f}$

$∴$ $ϕ_{d} - ϕ_{f} = ϕ_{c} - ϕ_{e}$

Q 6 :

The figure shows a surface XY separating two transparent media, medium-1 and medium-2. The lines ab and cd represent wavefronts of a light wave travelling in medium-1 and incident on XY. The lines ef and gh represent wavefronts of the light wave in medium-2 after refraction. [2007]

[IMAGE 1176]

Q. Speed of light is

the same in medium-1 and medium-2
larger in medium-1 than in medium-2
larger in medium-2 than in medium-1
different at $b$ and $d$ .

1

2

3

4

(2)

From the figure, the gap between consecutive wavefronts in medium 2 is less than that in medium 1. Hence, the wavelength of light in medium 2 is less than that in medium 1. Therefore, the speed of light $(v = f λ)$ in medium 1 is greater than that in medium 2.

Topic Question Set

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	Column I		Column II
(A)	Intensity of light received by lens	(p)	Radius of aperture
(B)	Angular magnification	(q)	Dispersion of lens
(C)	Length of telescope	(r)	Focal length of objective lens and eyepiece lens
(D)	Sharpness of image	(s)	Spherical aberration