Geometrical Optics | Physics JEE previous year questions with Solutions

Q 1 :
Given below are two statements:

Statement I: When the white light passed through a prism, the red light bends lesser than yellow and violet.

Statement II: The refractive indices are different for different wavelengths in dispersive medium.

In the light of the above statements, choose the correct answer from the options given below: [2024]

Statement I is false but Statement II is true
Statement I is true but Statement II is false
Both Statement I and Statement II are false
Both Statement I and Statement II are true

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2

3

4

(4)

As $λ_{r e d} > λ_{y e l l o w} > λ_{v i o l e t}$

Light ray with longer wavelength bends less. So red has minimum wavelength so least bends.

Q 2 :
If the refractive index of the material of a prism is cot(A/2), where A is the angle of prism then the angle of minimum deviation will be [2024]

$π - 2 A$
$\frac{π}{2} - 2 A$
$π - A$
$\frac{π}{2} - A$

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4

(1)

$\cos \frac{A}{2} = \sin (\frac{A + δ_{m i n}}{2})$

$\frac{A + δ_{m i n}}{2} = \frac{π}{2} - \frac{A}{2}$

$δ_{m i n} = π - 2 A$

Q 3 :
The refractive index of a prism with apex angle A is cot A/2. The angle of minimum deviation is [2024]

$δ_{m} = 180^{o} - 4 A$
$δ_{m} = 180^{o} - 3 A$
$δ_{m} = 180^{o} - 2 A$
$δ_{m} = 180^{o} - A$

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(3)

$μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin \frac{A}{2}}$

$\frac{\cos \frac{A}{2}}{\sin \frac{A}{2}} = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin \frac{A}{2}}$

$\sin (\frac{π}{2} - \frac{A}{2}) = \sin (\frac{A + δ_{m}}{2})$

$\frac{π}{2} - \frac{A}{2} = \frac{A}{2} + \frac{δ_{m}}{2} \Rightarrow δ_{m} = π - 2 A$

Q 4 :
The refractive index of prism is $μ = \sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _____°. [2024]

0%

(60)

$δ = i + e - A and \frac{δ}{A} = 1; δ = A$

$A = i + e - A$

$i + e = 2 A and for δ_{min}, i = e$

$So, i = e = A$

$By Snell's law at the first surface of prism$

$1 \cdot \sin A = \sqrt{3} \cdot \sin (\frac{A}{2}) \Rightarrow A = 60 °$

Q 5 :
The refractive index of the material of glass prism is $\sqrt{3}$ . The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism? [2025]

50°
60°
58°
48°

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(2)

$μ = \frac{\sin (\frac{A + δ_{\min}}{2})}{\sin \frac{A}{2}}$

Given $δ_{\min} = A$

$\sqrt{3} = \frac{\sin A}{\sin \frac{A}{2}} = \frac{2 \sin \frac{A}{2} \cos \frac{A}{2}}{\sin \frac{A}{2}}$

$\cos \frac{A}{2} = \frac{\sqrt{3}}{2} \Rightarrow A = 60 °$

Q 6 :
A thin prism $P_{1}$ with angle 4° made of glass having refractive index 1.54, is combined with another thin prism $P_{2}$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $P_{2}$ in degree is [2025]

4
3
16/3
1.5

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(2)

For dispersion without deviation, $δ_{net} = 0$

$(μ_{1} - 1) A_{1} = (μ_{2} - 1) A_{2}$

$\Rightarrow (1.54 - 1) 4 ° = (1.72 - 1) A_{2}$

or $A_{2} = \frac{0.54}{0.72} \times 4 = 3 °$

Q 7 :
Consider following statements for refraction of light through prism, when angle of deviation is minimum.

(A) The refracted ray inside prism becomes parallel to the base.

(B) Larger angle prisms provide smaller angle of minimum deviation.

(C) Angle of incidence and angle of emergence becomes equal.

(D) There are always two sets of angles of incidence for which deviation will be same except at minimum deviation setting.

(E) Angle of refraction becomes double of prism angle.

Choose the correct answer from the options given below: [2025]

A, C and D Only
B, C and D Only
A, B and E Only
B, D and E Only

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(1)

Because of symmetry where i = r, and $r = \frac{A}{2}$

$δ = (μ - 1) A$

(A) is correct

(B) is incorrect

(C) is correct

(D) is correct as $δ = i + e - A$

(E) is incorrect

Q 8 :
A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to 60°. The refractive index of the prism material is $\sqrt{2}$ . The angle of incidence (in degrees) is __________. [2025]

0%

(45)

For minimum deviation $r_{1} = r_{2} = \frac{A}{2} = 30 °$

At P, $1 \times \sin i = μ \times \sin 30$

$\sin i = \sqrt{2} \times \frac{1}{2} = \frac{1}{\sqrt{2}} \Rightarrow i = 45 °$

Topic Question Set

Q 2 :
If the refractive index of the material of a prism is cot(A/2), where A is the angle of prism then the angle of minimum deviation will be [2024]

Q 3 :
The refractive index of a prism with apex angle A is cot A/2. The angle of minimum deviation is [2024]

Q 4 :
The refractive index of prism is $μ = \sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _____°. [2024]

0%

Q 5 :
The refractive index of the material of glass prism is $\sqrt{3}$ . The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism? [2025]

Q 6 :
A thin prism $P_{1}$ with angle 4° made of glass having refractive index 1.54, is combined with another thin prism $P_{2}$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $P_{2}$ in degree is [2025]

Q 8 :
A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to 60°. The refractive index of the prism material is $\sqrt{2}$ . The angle of incidence (in degrees) is __________. [2025]

0%

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Topic Question Set

Q 2 : If the refractive index of the material of a prism is cot(A/2), where A is the angle of prism then the angle of minimum deviation will be [2024]

Q 3 : The refractive index of a prism with apex angle A is cot A/2. The angle of minimum deviation is [2024]

Q 4 : The refractive index of prism is μ=3 and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _____°. [2024]

0%

Q 5 : The refractive index of the material of glass prism is 3. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism? [2025]

Q 6 : A thin prism P1 with angle 4° made of glass having refractive index 1.54, is combined with another thin prism P2 made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism P2 in degree is [2025]

Q 8 : A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to 60°. The refractive index of the prism material is 2. The angle of incidence (in degrees) is __________. [2025]

0%

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Q 2 :
If the refractive index of the material of a prism is cot(A/2), where A is the angle of prism then the angle of minimum deviation will be [2024]

Q 3 :
The refractive index of a prism with apex angle A is cot A/2. The angle of minimum deviation is [2024]

Q 4 :
The refractive index of prism is $μ = \sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _____°. [2024]

Q 5 :
The refractive index of the material of glass prism is $\sqrt{3}$ . The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism? [2025]

Q 6 :
A thin prism $P_{1}$ with angle 4° made of glass having refractive index 1.54, is combined with another thin prism $P_{2}$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $P_{2}$ in degree is [2025]

Q 8 :
A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to 60°. The refractive index of the prism material is $\sqrt{2}$ . The angle of incidence (in degrees) is __________. [2025]