A convex lens made of glass (refractive index = 1.5) had focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to [2025]

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Solution

Q.
A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to [2025]

1 72 cm

2 96 cm

3 24 cm

4 48 cm

Ans.
(2)

$\frac{1}{24} = (\frac{μ_{l}}{μ_{s}} - 1) [\frac{1}{R_{1}} - \frac{1}{R_{2}}]$

$\frac{1}{24} = (1.5 - 1) [\frac{2}{R}]$ ... (i)

$\frac{1}{f'} = (\frac{1.5}{1.33} - 1) (\frac{2}{R})$ ... (ii)

(i) divided by (ii), $\frac{f'}{24} = 4 \Rightarrow f' = 96 cm$

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