There is a spherical glass ball of refractive index $μ_{1}$ and another glass ball of refractive index $μ_{2}$ inside it 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 the outer surface of the ball at an angle $i_{1}$ . Mark the correct options.

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The value of $r_{1}$ is $\sin^{- 1} (\frac{\sin i_{1}}{μ_{1}})$

The value of $r_{2}$ is $\sin^{- 1} (\frac{R_{1}}{μ_{2} R_{2}} \sin i_{1})$

The value of $r_{1}$ is $\sin^{- 1} (\frac{\sin i_{2}}{μ_{2}})$

The value of $r_{2}$ is $\sin^{- 1} (\frac{R_{2}}{μ_{2} R_{1}} \sin i_{1})$

answer is A, B.

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Detailed Solution

$μ_{1} \sin r_{1} = \sin i_{1} \Rightarrow r_{1} = \sin^{- 1} (\frac{\sin i_{1}}{μ_{1}}) \frac{μ_{1}}{μ_{2}} \sin i_{2} = \sin r_{2} \frac{μ_{1}}{μ_{2}} \frac{R_{1}}{R_{2}} \frac{\sin i_{1}}{μ_{1}} = \sin r_{2} r_{2} = \sin^{- 1} (\frac{R_{1}}{μ_{2} R_{2}} \sin i_{1})$