A spherical transparent medium of refractive index n is placed in air. A thin parallel beam of light of monochromatic wavelength λ is incident at a point O of the sphere at an angle of incident i. Then which of the following statements will be true for this optic system?

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A spherical transparent medium of refractive index $n$ is placed in air. A thin parallel beam of light of monochromatic wavelength $λ$ is incident at a point O of the sphere at an angle of incident $i$ . Then which of the following statements will be true for this optic system?

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If the angle $i = 90^{0}$ (grazing incidence) the emergent ray will come out grazing the surface.

If the angle of incident i such that the angle of refraction at O is equal to the critical angle C for the medium of sphere, the emergent ray will be parallel to the incident ray.

For the ray to come out of the sphere after refraction through it, the incident angle i should be less than the critical angle C for the medium of the sphere.

The angle of emergence $θ$ (made with the normal) for the ray will be equal to the incident angle i for all values of i.

answer is B, C.

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Detailed Solution

The diagram shows the path of a ray AB incident at B on the sphere at angle i. The path ABCD shows is refracted ray BC, inside the sphere with angle r of refraction and the emergent ray CD with angle of emergence i.

Obviously $∠ O B C = ∠ O C B = r$
Hence $∠ A B N = ∠ D C M = i$ for all values of i.
Also, if $∠ A B N = 90^{0}$ , grazing incident at B, then
$∠ D C M = 90^{0}$ , grazing emergence at C.
But AB and CD will not be parallel.