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 `i_(2)`

Options

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

Answer

C

Explanation

Using sine rule `("sin"r_(1))/(R_(2)) = ("sin"(180-i_(2)))/(R_(1)) implies "sin" i_(2) = (R_(1))/(R_(2)) "sin"r_(1) = ((R_(1))/(R_(2))("sin"i_(1))/(mu_(1))) implies i_(2) = sin^(-1)((R_(1))/(R_(2)) ("sin"i_(1))/(mu_(1)))`