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Physics Question on Reflection Of Light By Spherical Mirrors

The critical angle for glass-water boundary is C. If μg=1.5{{\mu }_{g}}=1.5 1.5 and μω=43{{\mu }_{\omega }}=\frac{4}{3} then the value of C is:

A

sin⁡−1(32){{\sin }^{-1}}\left( \frac{3}{2} \right)

B

sin⁡−1(43){{\sin }^{-1}}\left( \frac{4}{3} \right)

C

sin⁡−1(89){{\sin }^{-1}}\left( \frac{8}{9} \right)

D

sin⁡−1(12){{\sin }^{-1}}\left( \frac{1}{2} \right)

Answer

sin⁡−1(89){{\sin }^{-1}}\left( \frac{8}{9} \right)

Explanation

Solution

From the relation sin⁡C=μwμg=4/33/2=89\sin C=\frac{{{\mu }_{w}}}{{{\mu }_{g}}}=\frac{4/3}{3/2}=\frac{8}{9} C=sin⁡−189C={{\sin }^{-1}}\frac{8}{9}