Question

A glass prism of refractive index $1.5$ is $A$ immersed in water of refractive index $ \frac{4}{3.} $ A light incident normally on the face $AB$ is totally reflected to reach the face $AC$, if :

• A. $ \sin \,\theta \,>\frac{3}{2} $
• B. $ \sin \,\theta \,>\frac{2}{3} $
• C. $ \sin \,\theta \,>\frac{8}{9} $
• D. $ \frac{2}{3}\sin \,\theta \,>\frac{8}{9} $

Answer 1

Answer: (C)

Key Idea: There will be total internal reflection at face AC.
The critical angle is the angle of incidence I the denser medium for which the angle of refraction in the rarer medium is $ 90^{\circ}.$
From Snells law
$ _{g}{{n}_{w}}=\frac{\sin C}{\sin {{90}^{o}}} $
$ \Rightarrow $ $ \sin C=\frac{_{a}{{n}_{w}}}{_{a}{{n}_{g}}}=\frac{4/3}{1.5} $
$ =\frac{8}{9} $
For total internal reflection $ \theta >C $ .
$ \therefore \sin \theta >\frac{8}{9} $ .