If a light Ray incident normally on one of the faces of the prism of refractive index 2 and emergence ray just grazes the second face of the prism , then the angle of deviation
Answers
If a ray of light is incident normally on one of the faces of a prism whose apex angle is 30o and refractive index is 2–√,
then what is the deviation of the ray?
The ray is incident normal to the first surface.
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The ray does not deviate when it enters the prism.
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The ray strikes the second surface of the prism from inside at an angle 30o to the normal since the apex angle of the prism is 30o.
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The angle of incidence inside the prism is i=30o.
The refractive index of the material of the prism with respect to air is 2–√.
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The refractive index of air with respect to the material of the prism is μ=12√.
Let r
be the angle of refraction when the ray emerges from the prism.
sinisinr=μ⇒sin30osinr=12√.
⇒sinr=2–√sin30o=12√.
⇒r=arcsin(12√)=45o.
The ray is deviated only when it passes through the second surface.
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The angle of deviation of the ray is 45o−30o=15