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Prism refraction: NEET MCQs with answers

49 questions on this topic of Optics (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. A ray of light passes through a glass prism of refracting angle 60°. The angle of incidence is 35° and the angle of emergence is 79°. The angle of deviation suffered by the ray is:

  1. 44°
  2. 54°
  3. 64°
  4. 34°
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Answer: (B) 54°

For any prism, the relation connecting the angles is i + e = A + δ. Substituting the given values, 35° + 79° = 60° + δ. Hence, δ = 114° - 60° = 54°.

medium

2. A ray of light is incident at an angle i on one face of an equilateral prism. It is found that the emergent ray grazes the second face. If the refractive index of the prism material is 2/√3, what is the value of the angle of incidence i?

  1. 0°
  2. 30°
  3. 45°
  4. 60°
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Answer: (A) 0°

For grazing emergence at the second face, e = 90°, so r₂ = c where sin c = 1/μ = √3/2, which gives r₂ = 60°. Since the prism is equilateral, A = 60° and A = r₁ + r₂, leading to r₁ = A - r₂ = 60° - 60° = 0°. By Snell's law at the first face, sin i = μ sin r₁ = μ sin 0° = 0, hence i = 0°.

hard

3. A ray of light is incident at an angle i on one face of a prism of refracting angle A = 75° and refractive index μ = √2. If the ray just undergoes total internal reflection at the second face, the angle of incidence i must be:

  1. 60°
  2. 30°
  3. 45°
  4. 0°
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Answer: (C) 45°

For total internal reflection to just occur at the second surface, r₂ equals the critical angle C. Here sin C = 1/μ = 1/√2, so C = 45°. Since A = r₁ + r₂, we have r₁ = A - C = 75° - 45° = 30°. Applying Snell's law at the first face: sin i = μ sin r₁ = √2 × sin 30° = √2 × (1/2) = 1/√2. Thus, i = 45°.

medium

4. The refracting angle of a glass prism is 60° and its refractive index is √3. If a ray of light is incident at 60° on one face, the angle of emergence from the other face is:

  1. 60°
  2. 45°
  3. 30°
  4. 90°
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Answer: (A) 60°

By Snell's law at the first surface, 1 × sin 60° = √3 × sin r₁, giving sin r₁ = (√3/2)/√3 = 1/2, so r₁ = 30°. Then r₂ = A - r₁ = 60° - 30° = 30°. At the second surface, √3 × sin 30° = 1 × sin e, giving sin e = √3/2, which means e = 60°.

easy

5. Consider the following two statements regarding refraction through a triangular prism: Statement I: The angle of deviation decreases continuously with an increase in the angle of incidence. Statement II: Inside an equilateral prism set for minimum deviation, the refracted ray is parallel to the base of the prism. Choose the correct option:

  1. Both Statement I and Statement II are correct.
  2. Statement I is correct but Statement II is incorrect.
  3. Statement I is incorrect but Statement II is correct.
  4. Both Statement I and Statement II are incorrect.
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Answer: (C) Statement I is incorrect but Statement II is correct.

Statement I is incorrect because the deviation first decreases with increasing angle of incidence, attains a minimum value (δm), and then increases. Statement II is correct because for an equilateral prism at minimum deviation, r₁ = r₂ = 30°, making the refracted ray parallel to the base.

hard

6. A prism of refractive index μ and refracting angle A produces a minimum deviation equal to A. If the prism is placed in a medium of refractive index μ/2, what will be the new value of the refractive index of the prism relative to this surrounding medium?

  1. 1
  2. 2 cos(A/2)
  3. 2 sin(A/2)
  4. 2
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Answer: (D) 2

The relative refractive index of the prism in the new medium is μ_rel = μ / (μ/2) = 2. This is independent of the value of A and is purely determined by the ratio of the refractive indices.

easy

7. A thin prism of refracting angle A = 5° is made of a glass of refractive index μ = 1.6. The angle of deviation produced by this prism for a ray of light incident at a small angle is:

  1. 2.0°
  2. 1.5°
  3. 4.0°
  4. 3.0°
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Answer: (D) 3.0°

For a thin prism of small refracting angle A, the deviation δ is given by the formula δ = (μ - 1)A. Here, δ = (1.6 - 1) × 5° = 0.6 × 5° = 3.0°.

easy

8. The refracting angle of a prism is A and the refractive index of its material is cot(A/2). The angle of minimum deviation produced by this prism is:

  1. 180° - A
  2. 90° - A
  3. 180° - 2A
  4. 180° - 3A
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Answer: (C) 180° - 2A

Using the prism formula, μ = sin((A + δm)/2) / sin(A/2). Given μ = cot(A/2) = cos(A/2)/sin(A/2), we get sin((A + δm)/2) = cos(A/2) = sin(90° - A/2). Therefore, (A + δm)/2 = 90° - A/2, which simplifies to δm = 180° - 2A.

medium

9. Consider the following statements regarding refraction through a glass prism: Statement I: The angle of deviation is minimum when the path of light inside an equilateral prism is parallel to its base. Statement II: For any angle of deviation other than the minimum deviation, there are two distinct angles of incidence corresponding to the same deviation. Choose the correct option:

  1. Both Statement I and Statement II are true.
  2. Both Statement I and Statement II are false.
  3. Statement I is true but Statement II is false.
  4. Statement I is false but Statement II is true.
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Answer: (A) Both Statement I and Statement II are true.

At minimum deviation in an equilateral (or isosceles) prism, r₁ = r₂ = A/2, making the refracted ray parallel to the base. By the principle of reversibility of light, reversing the path interchanges i and e, meaning two angles of incidence (i and e) give the same deviation δ when δ > δm. Thus, both statements are true.

hard

10. A glass prism has a refracting angle A = 75° and refractive index μ = √2. A monochromatic light ray enters the first surface. The angle of incidence i such that the ray just grazes the second surface (e = 90°) is:

  1. 45°
  2. 30°
  3. 60°
  4. 0°
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Answer: (A) 45°

At the second surface, grazing emergence means the angle of incidence inside the glass is equal to the critical angle C. Here sin(C) = 1/μ = 1/√2, so r₂ = 45°. Since r₁ + r₂ = A = 75°, we have r₁ = 75° - 45° = 30°. Applying Snell's law at the first surface: sin(i) = μ sin(r₁) = √2 × sin(30°) = √2 × (1/2) = 1/√2, giving i = 45°.

easy

11. A ray of light passes through an equilateral glass prism such that the angle of incidence is equal to the angle of emergence. If the angle of emergence is 3/4 times the angle of the prism, the angle of deviation suffered by the ray is:

  1. 60°
  2. 45°
  3. 30°
  4. 15°
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Answer: (C) 30°

For an equilateral prism, A = 60°. Given i = e = (3/4)A = (3/4) × 60° = 45°. Using the prism relation i + e = A + δ, we get 45° + 45° = 60° + δ, which yields δ = 90° - 60° = 30°.

easy

12. Consider the following statements regarding refraction through a glass prism: Statement I: Inside an equilateral prism set in the minimum deviation position, the refracted ray is always parallel to the base of the prism. Statement II: In any prism, minimum deviation occurs when the angle of incidence is equal to the angle of emergence. In the light of the above statements, choose the most appropriate answer from the options given below:

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (A) Both Statement I and Statement II are correct

At minimum deviation, the ray passes symmetrically through the prism, meaning i = e and r₁ = r₂ = A/2. For an equilateral (or isosceles) prism, symmetry ensures that the internal refracted ray travels parallel to the base. Thus, both statements are correct.

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