A lens having refractive index 1.6 has focal length of 12 cm , when...

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)

Options

A355 mm
B288 mm
C555 mm
D655 mm

Correct answer

B. 288 mm

Step-by-step solution

As we know,

\frac{1}{\mathrm{f}}=\left[\frac{\mu_{\mathrm{L}}}{\mu_

{

\mathrm{m}

}

}-1\right]\left[\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right]

For air

\mu_{\mathrm{m}}=1

\begin{aligned} & \frac{1}{12}=[1.6-1]\left[\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right] \\ & \frac{1}{12}=\frac{6}{10}\left[\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right] \\ & {\left[\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right]=\frac{10}{72}}\end{aligned}

For water

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

\begin{aligned} & \frac{1}{\mathrm{f}}=\frac{1}{4} \times \frac{10}{72} \\ & \mathrm{f}=28.8 \mathrm{~cm} \\ & \mathrm{f}=288 \mathrm{~mm}\end{aligned}

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