Ray optics

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Question

Focal length of a convex lens in air is 10 cm. Find its focal length in water. Given $μ_{g} = 3 / 2 and μ_{w} = 4 / 3$

Moderate

Solution

$\begin{array}{l} \frac{1}{f} = (\frac{μ_{l}}{μ_{s u r r}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) \\ \frac{f_{w a t e r}}{f_{a i r}} = \frac{(μ_{g} - 1)}{(\frac{μ_{g}}{μ_{w}} - 1)} = \frac{(3 / 2 - 1)}{(\frac{3 / 2}{4 / 3} - 1)} \\ f_{w} = 4 f_{a i r} = 40 c m \end{array}$

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