A right angled triangular prism of refractive index `mu_(1)` is kept floating on a liquid (surface) having refractive index `mu_(2)`. The condition such tat light incident normally passes through base of prism as shown in figure.

Options

A. `mu_(1)=Cos2theta//Costheta`
B. `mu_(2)=Cos2theta//Costheta`
C. `mu_(1)=Sin2theta//Costheta`
D. `mu_(2)=Sin2theta//Sintheta`

Answer

B

Explanation

`sin(90-theta)=(1)/(mu_(1))impliescostheta=(1)/(mu_(1))to(1)`
`sin(90-2theta)=(1)/((mu_(1)//mu_(2)))`
`cos2theta=(mu_(2))/(mu_(1))=(mu_(2))/((1//costheta))thereforemu_(2)=(cos2theta)/(costheta)`