A transparent cube of side d, made of a material of refractive index `mu_(2)` , is immersed in a liquid of refractive index `mu_(1)(mu_(1)ltmu_(2))`. . A ray is incident on the face AV at an angle `theta` (shown in the figure). Total internal refraction takes place at point E on the face BC. Then must satisfy:

Options

A. `theta gt "sin"^(-1)(mu_(1))/(mu_(2))`
B. `theta lt "sin"^(-1)sqrt((mu_(2)^(2))/(mu_(1)^(2))-1)`
C. `theta lt "sin"^(-1)(mu_(1))/(mu_(2))`
D. `theta gt sin^(-1)sqrt((mu_(2)^(2))/(mu_(1)^(2))-1)`

Answer

B

Explanation

`90-rge theta_(C)`
`90-r ge sin^(-1)((mu_(1))/(mu_(2)))impliescos r ge (mu_(1))/(mu_(2))` Snell's law

`(sin theta)/(sin r)=(mu_(2))/(mu_(1))implies sin theta=(mu_(2))/(mu_(1)) sin r=(mu_(2))/(mu_(1)) sqrt(1-((mu_(1))/(mu_(2)))^(2))`
`sin theta=sqrt(((mu_(2))/(mu_(1)))^(2)-1)`
This is maximum `theta` so `theta le sqrt(((mu_(2))/(mu_(1)))^(2)-1)`