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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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.

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.

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.