There is an air lens in an extended glass medium. The radius of curvature of both the curved surfaces is R, and refractive index of the glass is 32. Power of this air lens is P. Find the refractive index of the material to be filled inside the lens so that power becomes -P

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There is an air lens in an extended glass medium. The radius of curvature of both the curved surfaces is R, and refractive index of the glass is $\frac{3}{2}$ . Power of this air lens is $P$ . Find the refractive index of the material to be filled inside the lens so that power becomes $- P$

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answer is 2.

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Detailed Solution

For air lens $P = (\frac{μ_{a}}{μ_{g}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$
$= (\frac{1}{3 / 2} - 1) (\frac{2}{R}) = - \frac{2}{3 R}$
If a material of refractive index $μ$ is filled in the cavity
$P' = (\frac{2 μ}{3} - 1) (\frac{2}{R}) \frac{2}{3 R} = (\frac{2 μ}{3} - 1) \frac{2}{R} \begin{array}{l} \Rightarrow 1 = 2 μ - 3 \\ \Rightarrow μ = 2 \end{array}$