First slide

The lens

Question

A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{1}$ then the ratio $f_{1} / f$ is closest to the integer:

Moderate

A

9
B

17
C

1
D

5

Solution

$\begin{array}{l} A p p l y L e n s M a k e r F o r m u l a w h e n l e n s i s i n a i r \\ \frac{1}{f_{a}} = (\frac{μ_{0}}{μ_{a}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) \\ A p p l y L e n s M a k e r F o r m u l a w h e n l e n s i s i n m e d i u m \\ \frac{1}{f_{m}} = (\frac{μ_{0}}{μ_{m}} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) \\ \Rightarrow \frac{f_{a}}{f_{m}} = \frac{(\frac{μ_{0}}{μ_{m}} - 1)}{(\frac{μ_{0}}{μ_{a}} - 1)} = \frac{(\frac{1.50}{1.42} - 1)}{[\frac{1.50}{1} - 1]} = \frac{0.08}{(1.42) (0.5)} \\ \Rightarrow \frac{f_{m}}{f_{a}} = \frac{(1.42) (0.5)}{0.08} = 8.875 \approx 9 \end{array}$

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