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JEE MAIN_2026
06-04-26_S1
Question
A spherical interface lens of radius R separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of 4R in front of spherical interface. The magnitude of the magnification of point source image is _____ .
Question Image
Select the correct option:
A
1.66
B
2.33
C
2.66
D
1.33
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Solution
$\begin{aligned} & \mathrm{m}=\frac{\mathrm{n}_1}{\mathrm{n}_2} \frac{\mathrm{v}}{\mathrm{u}} \\ & \frac{\mathrm{n}_2}{\mathrm{v}}-\frac{\mathrm{n}_1}{\mathrm{u}}=\frac{\mathrm{n}_2-\mathrm{n}_1}{\mathrm{R}} \\ & \frac{1.4}{\mathrm{v}}+\frac{1}{4 \mathrm{R}}=\frac{1.4-1}{\mathrm{R}} \\ & \frac{1.4}{\mathrm{v}}=\frac{4}{10 \mathrm{R}}-\frac{1}{4 \mathrm{R}} \\ & \mathrm{v}=\frac{56 \mathrm{R}}{6}=+\frac{28}{3} \mathrm{R} \\ & \mathrm{m}=\frac{1}{1.4} \cdot \frac{28 \mathrm{R} / 3}{(-4 \mathrm{R})}=-1.67\end{aligned}$
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