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Geometrical Optics question

2018 · 16 Apr · Shift 1 · Q52
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  5. /2018 · 16 Apr · Shift 1 · Q52

Geometrical Optics question

2018 · 16 Apr · Shift 1 · Q52

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
A ray of light is incident at an angle of 60o on one face of a prism of angle 30o. The emergent ray of light makes an angle of 30o with incident ray. The angle made by the emergent ray with second face of prism will be :
  1. A
    0o
  2. B
    90o
  3. C
    45o
  4. D
    30o
View written solutionFree

Correct answer: B

  1. Given data
  • Angle of prism: A=30∘A = 30^\circA=30∘
  • Angle of incidence on first face: i=60∘i = 60^\circi=60∘
  • Angle between incident ray and emergent ray: 30∘30^\circ30∘

We need the angle made by the emergent ray with the second face.

  1. Use the prism deviation relation

For a prism, the angle between the direction of the incident ray and emergent ray is the angle of deviation δ\deltaδ.

So here,

δ=30∘\delta = 30^\circδ=30∘

For a prism,

δ=i+e−A\delta = i + e - Aδ=i+e−A

where eee is the angle of emergence with the normal to the second face.

Substitute the values:

30∘=60∘+e−30∘30^\circ = 60^\circ + e - 30^\circ30∘=60∘+e−30∘ 30∘=30∘+e30^\circ = 30^\circ + e30∘=30∘+e e=0∘e = 0^\circe=0∘

So the emergent ray makes an angle 0∘0^\circ0∘ with the normal to the second face.

  1. Convert to angle with the second face

Angle with the face =90∘−= 90^\circ -=90∘− angle with the normal.

Thus,

angle with second face=90∘−0∘=90∘\text{angle with second face} = 90^\circ - 0^\circ = 90^\circangle with second face=90∘−0∘=90∘
  1. Check options
  • A: 0∘0^\circ0∘ →\to→ incorrect
  • B: 90∘90^\circ90∘ →\to→ correct
  • C: 45∘45^\circ45∘ →\to→ incorrect
  • D: 30∘30^\circ30∘ →\to→ incorrect
  1. Final answer

The emergent ray is perpendicular to the second face, so it makes an angle of

90∘90^\circ90∘

with the second face.

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