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}

then the radius of curvature of meniscus is : $In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex$

Options

A $\frac{1}{3} \mathrm{~cm}$
B $\frac{4}{3} \mathrm{~cm}$
C $1\mathrm{~cm}$
D $\frac{2}{3} \mathrm{~cm}$

Correct answer

D. $\frac{2}{3} \mathrm{~cm}$

Step-by-step solution

$In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex$

\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}

Practice Ray Optics on Quantrex Academy →

More from Ray Optics

A double convex lens made of glass of refractive index 1.5 and radii of curvature of the… JEE Advanced 2026 A beam of polychromatic light passes through a thin prism of prism angle 6^∘ . The… JEE Advanced 2026 Consider two isosceles prisms 1 and 2 with prism angles A_1 and A_2 and refractive… JEE Advanced 2026 A thin biconvex lens is prepared from the glass ( μ=1.5 ) both curved surfaces of which… JEE Main 2026 Light ray incident along a vector AO ( AO = 2 i -3 j ) emerges out along vector OB ( OB =… JEE Main 2026 Angle of minimum deviation is equal to the half of the angle of prism in an equilateral… JEE Main 2026 A concave mirror of focal length 10 cm forms an image which is double the size of object… JEE Main 2026 A spherical interface lens of radius R separates two media of refractive indices 1 and… JEE Main 2026 Full Ray Optics list All JEE Main PYQs