Question 112: Ray Optics

Question

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 ${ }^{\prime}-2^{\prime}$ then the radius of curvature of meniscus is :

Accepted Answer

$$\begin{aligned}
& \frac{\mathrm{n}_2}{\mathrm{v}}-\frac{\mathrm{n}_1}{\mathrm{u}} \frac{\mathrm{n}_2-\mathrm{n}_1}{\mathrm{R}} \
& \frac{1.4}{\mathrm{v}}-\frac{1.3}{-13}=\frac{0.1}{\mathrm{R}} \
& \frac{1.4}{\mathrm{v}}=\frac{1-\mathrm{R}}{10 \mathrm{R}} \
& \frac{1.4}{\mathrm{v}}=\frac{1-\mathrm{R}}{10 \mathrm{R}} \
& \mathrm{~m}=\frac{\mathrm{v} / \mathrm{n}_2}{\mathrm{u} / \mathrm{n}_1} \
& -2 	imes \frac{(-13)}{1.3}=\frac{10 \mathrm{R}}{1-\mathrm{R}} \
& \mathrm{R}=\frac{2}{3} \mathrm{~cm}
\end{aligned}$$

Answer

$ \frac{2}{3} 	ext{ cm} $

Answer

$ \frac{4}{3} 	ext{ cm} $

Answer

$ \frac{1}{3} 	ext{ cm} $

Answer

1 cm

Ray Optics

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