Q61 / 75 · JEE Main 2025 (29 Jan Shift 2) · Physics

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

  • A
    24 cm
  • Correct answer
    B
    96 cm
  • C
    48 cm
  • D
    72 cm

Solution

$\begin{aligned} & \frac{1}{8}=\left(\frac{\mu_{\ell}}{\mu_{\mathrm{s}}}-1\right)\left[\frac{1}{\mathrm{R}_1}-\frac{1}{\mathrm{R}_2}\right] \\ & \frac{1}{24}=(1.5-1)\left[\frac{2}{\mathrm{R}}\right] ...(i)\\ & \frac{1}{\mathrm{f}^{\prime}}=\left(\frac{1.5}{1.33}-1\right)\left(\frac{2}{\mathrm{R}}\right) \\ & \frac{1}{\mathrm{f}^{\prime}}=\left(\frac{1.5 \times 3}{4}-1\right) \frac{2}{\mathrm{R}}...(ii) \end{aligned}$ (i) divided by (ii) $\begin{aligned} & \frac{\mathrm{f}^{\prime}}{24}=4 \\ & \mathrm{f}^{\prime}=96 \mathrm{~cm} \end{aligned}$

Hence, the correct answer is option: 'B'.

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