Geometrical Optics

A solid glass sphere of refractive index n=√3 and radius R contains a spherical air cavity of radius ‌

R

2

, as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index n=1 ) remains inside the glass sphere. An unpolarized, unidirectional and monochromatic light source S emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point O and is fully polarized, then the angle of incidence at the inner surface of the glass sphere is θ. The value of sin‌θ is _______