A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach on the face BC if.

Options

A. `sinthetale(2)/(3)`
B. `costhetage(8)/(9)`
C. `sinthetagt(8)/(9)`
D. `costhetale(8)/(9)`

Answer

C

Explanation

Here, `.^(a)mu_(g)=1.5=(3)/(2),.^(a)mu_(w)=(4)/(3)`
`:..^(w)mu_(g)=(.^(a)mu_(g))/(.^(a)mu_(w))=(3//2)/(4//3)=(9)/(8)`
As, `sinC=(1)/(.^(w)mu_(g))=(1)/(9//8)=(8)/(9)impliesC=sin^(-1)((8)/(9))`
For total internal reflection, `thetagtC`
`thetagtsin^(-1)((8)/(9))` or `sinthetagt(8)/(9)`