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QJEEM25Phed58: JEE Main 2025 Physics - Class 12 JEEM25Phed58 Solution: In a long glass tube, mixture of two liquids A and B with…

In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A . If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of ′−2′{ }^{\prime}-2^{\prime} then the radius of curvature of meniscus is :

Multiple Choice Options

  • A 23 cm\frac{2}{3} \text{ cm}
  • B 43 cm\frac{4}{3} \text{ cm}
  • C 13 cm\frac{1}{3} \text{ cm}
  • D 1 cm

Step-by-Step Verified Solution

JEE Main 2025 (Online) 28th January Evening Shift Physics - Geometrical Optics Question 13 English Explanation

amp;n2v−n1un2−n1Ramp;1.4v−1.3−13=0.1Ramp;1.4v=1−R10Ramp;1.4v=1−R10Ramp; m=v/n2u/n1amp;−2×(−13)1.3=10R1−Ramp;R=23 cm\begin{aligned}& \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{1.3}{-13}=\frac{0.1}{\mathrm{R}} \\& \frac{1.4}{\mathrm{v}}=\frac{1-\mathrm{R}}{10 \mathrm{R}} \\& \frac{1.4}{\mathrm{v}}=\frac{1-\mathrm{R}}{10 \mathrm{R}} \\& \mathrm{~m}=\frac{\mathrm{v} / \mathrm{n}_2}{\mathrm{u} / \mathrm{n}_1} \\& -2 \times \frac{(-13)}{1.3}=\frac{10 \mathrm{R}}{1-\mathrm{R}} \\& \mathrm{R}=\frac{2}{3} \mathrm{~cm}\end{aligned}

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