JEE Advanced Physics PYQ: Wave Optics | Previous Year Questions with Solutions

Q 1 :

A parallel beam of light strikes a piece of transparent glass having the cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale). [2020]

[IMAGE 1143]

[IMAGE 1144]
[IMAGE 1145]
[IMAGE 1146]
[IMAGE 1147]

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(1)

Clearly, the middle part of the glass is diverging and upper and lower parts are converging. Therefore, the correct shape of the emergent wavefront is as shown in the figure.

[IMAGE 1148]

Q 2 :

In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on $θ$ for constructive interference at P between the ray BP and reflected ray OP. [2003]

[IMAGE 1149]

$\cos θ = \frac{3 λ}{2 d}$
$\cos θ = \frac{λ}{4 d}$
$\sec θ - \cos θ = \frac{λ}{d}$
$\sec θ - \cos θ = \frac{4 λ}{d}$

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(2)

[IMAGE 1150]

In $∆ O P M$ ,

$O P = \frac{d}{\cos θ}$

In $∆ C O P$ ,

$O C = \frac{d \cos 2 θ}{\cos θ}$

Path difference between the two rays reaching P

$= C O + O P + \frac{λ}{2} = \frac{d \cos 2 θ}{\cos θ} + \frac{d}{\cos θ} + \frac{λ}{2}$

$= \frac{d}{\cos θ} (\cos 2 θ + 1) + \frac{λ}{2} = 2 d \cos θ + \frac{λ}{2}$

For constructive interference at $P$ , path difference $= n λ$

$∴$ $2 d \cos θ + \frac{λ}{2} = n λ$ $\Rightarrow \cos θ = \frac{(2 n - 1) λ}{4 d}$

For $n = 1$ , $\cos θ = \frac{λ}{4 d}$

Q 3 :

Two beams of light having intensities $I$ and $4 I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $π / 2$ at point $A$ and $π$ at point $B$ . Then the difference between the resultant intensities at $A$ and $B$ is [2001]

$2 I$
$4 I$
$5 I$
$7 I$

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(2)

As we know, $I = I_{1} + I_{2} + 2 \sqrt{I_{1}} \sqrt{I_{2}} \cos ϕ$

When phase difference is $π / 2$ ,

$I_{π / 2} = I + 4 I$ $\Rightarrow I_{π / 2} = 5 I$

Again, when $d$ phase difference is $π$ ,

$I_{π} = I + 4 I + 2 \sqrt{I} \sqrt{4 I} \cos π = I$

$∴$ $I_{π / 2} - I_{π} = 5 I - I = 4 I$

Q 4 :

A monochromatic light wave is incident normally on a glass slab of thickness $d$ , as shown in the figure. The refractive index of the slab increases linearly from $n_{1}$ to $n_{2}$ over the height $h$ . Which of the following statement(s) is(are) true about the light wave emerging out of the slab? [2023]

[IMAGE 1151]

It will deflect up by an angle $\tan^{- 1} [\frac{(n_{2}^{2} - n_{1}^{2}) d}{2 h}] .$
It will deflect up by an angle $\tan^{- 1} [\frac{(n_{2} - n_{1}) d}{h}] .$
It will not deflect.
The deflection angle depends only on $(n_{2} - n_{1})$ and not on the individual values of $n_{1}$ and $n_{2}$ .

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Select one or more options

(2, 4)

[IMAGE 1152]

From the figure, $n_{1} d + ℓ = n_{2} d$

$∴$ $ℓ = n_{2} d - n_{1} d = (n_{2} - n_{1}) d$

$∴$ $\tan θ = \frac{ℓ}{h} = \frac{(n_{2} - n_{1}) d}{h}$

$∴$ Light wave emerging out of the slab is deflected by an angle $θ = \tan^{- 1} [\frac{(n_{2} - n_{1}) d}{h}]$

It depends only on $(n_{2} - n_{1})$ and not on the individual values of $n_{1}$ and $n_{2}$ .

Q 5 :

Two coherent monochromatic point sources $S_{1}$ and $S_{2}$ of wavelength $λ = 600 nm$ are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance $d = 1.8 mm$ . This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $Δ θ$ . Which of the following options is/are correct? [2017]

[IMAGE 1153]

A dark spot will be formed at the point $P_{2}$
At $P_{2}$ the order of the fringe will be maximum
The total number of fringes produced between $P_{1}$ and $P_{2}$ in the first quadrant is close to 3000
The angular separation between two consecutive bright spots decreases as we move from $P_{1}$ to $P_{2}$ along the first quadrant

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Select one or more options

(2, 3)

At $P_{2}$ ,

$Δ x = 0 .$ So we will have maxima there. It will be very much like the central maxima in YDSE with $n = 0$ . So (1) is incorrect.

At $P_{1}$ ,

$Δ x = S_{1} P - S_{2} P = d = 1.8 mm$

For maxima, $Δ x = n λ$

$n = \frac{Δ x}{λ} = \frac{1.8 \times 10^{- 3}}{600 \times 10^{- 9}} = \frac{1.8}{600} \times 10^{6} = 3000$

So, the number of fringes between $P_{1}$ and $P_{2}$ will be 3000.

So, (3) is correct. And it will also be the highest order fringe.

So, (2) is correct.

As, for bright fringe, $d \cos θ = n λ$

$\Rightarrow - d \sin θ Δ θ = Δ n λ$

$\Rightarrow Δ θ = - \frac{(Δ n) λ}{d \sin θ}$

As we move from $P_{1}$ to $P_{2}$ , $θ ↓ ↓$ . So $\sin θ$ $↓ ↓$ . Therefore, $Δ θ$ $↑ ↑$ .

So, (4) is incorrect.

Topic Question Set

Q 1 :

A parallel beam of light strikes a piece of transparent glass having the cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale). [2020]

[IMAGE 1143]

Q 2 :

In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on $θ$ for constructive interference at P between the ray BP and reflected ray OP. [2003]

[IMAGE 1149]

Q 3 :

Two beams of light having intensities $I$ and $4 I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $π / 2$ at point $A$ and $π$ at point $B$ . Then the difference between the resultant intensities at $A$ and $B$ is [2001]

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Topic Question Set

Q 1 : A parallel beam of light strikes a piece of transparent glass having the cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale). [2020] [IMAGE 1143]

Q 2 : In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on θ for constructive interference at P between the ray BP and reflected ray OP. [2003] [IMAGE 1149]

Q 3 : Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at point A and π at point B. Then the difference between the resultant intensities at A and B is [2001]

Want Us to Email you About Special Offers & Updates?

Q 1 :

A parallel beam of light strikes a piece of transparent glass having the cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale). [2020]

[IMAGE 1143]

Q 2 :

In the adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. Find the condition on $θ$ for constructive interference at P between the ray BP and reflected ray OP. [2003]

[IMAGE 1149]

Q 3 :

Two beams of light having intensities $I$ and $4 I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $π / 2$ at point $A$ and $π$ at point $B$ . Then the difference between the resultant intensities at $A$ and $B$ is [2001]