There is a spherical glass ball of refractive index `mu_(1)` and another glass ball of refractive index `mu_(2)` inside as shown in figure . The radius of the outer ball is `R_(1)` and that of inner ball is `R_(2)`. A ray is incident on outer surface of the ball at an angle `i_(1)`,

Find the value of `r_(2)`

Options

A. `sin^(-1)((R_(1))/(mu_(2)R_(2)"sin"i_(1)))`
B. `sin^(-1)((R_(2))/(mu_(2)R_(1)"sin"i_(1)))`
C. `sin^(-1)((R_(1))/(mu_(1)R_(2)) (1)/("sin"i_(1)))`
D. `sin^(-1) ((R_(2))/(mu_(1)R_(1))"sin"i_(1))`

Answer

A

Explanation

`(mu_(1))/(mu_(2)) "sin"i_(2) = "sin"r_(2) , (mu_(1))/(mu_(2)) (R_(1))/(R_(2)) ("sin"i_(1))/(mu_(1)) = "sin"r_(2) , r_(2) = sin^(-1)((R)/(mu_(2)R_(2))"sin"i_(1))`