A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28) [2025]

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Solution

Q.
A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water.

(Take refractive index of water as 1.28) [2025]

1 355 mm

2 288 mm

3 555 mm

4 655 mm

Ans.
(2)

As we know,

$\frac{1}{f} = [\frac{μ_{L}}{μ_{m}} -] [\frac{1}{R_{1}} - \frac{1}{R_{2}}]$

For air $μ_{m} = 1$

$\frac{1}{12} = [1.6 - 1] [\frac{1}{R_{1}} - \frac{1}{R_{2}}]$

$\frac{1}{12} = \frac{6}{10} [\frac{1}{R_{1}} - \frac{1}{R_{2}}]$

$[\frac{1}{R_{1}} - \frac{1}{R_{2}}] = \frac{10}{72}$ ...(i)

For water, $μ_{m} = 1.28$

$\frac{1}{f} = [\frac{1.6}{1.28} - 1] [\frac{10}{72}] = \frac{32}{128} \times \frac{10}{72}$

$\frac{1}{f} = \frac{1}{4} \times \frac{10}{72} \Rightarrow f$ =28.8 cm = 288 mm

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