question_answer

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)  \[\frac{2}{3}\sin \,\theta \,>\frac{8}{9}\]

Correct Answer: C

Solution :

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°. 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 \[\theta >C\]. \[\therefore \] \[\sin \theta >\frac{8}{9}\].