Question

A small object placed in air at 24 cm from convex surface of a rod of glass (n = 1.5) of length 2R has a convex hemispherical surface with radius of curvature R = 8 cm and a flat surface(figure). Find the final distance of the image (in cm) from the plane surface.

• A. 48 cm
• B. 72 cm
• C. 32 cm
• D. 24 cm

Answer 1

The correct option is A 48 cm

Given : $n_2=1.5$, $n_1=1$ and $R=8$ cm

Object distance $u=-24$ cm

Using the formula for spherical lens : $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$\therefore$ $\frac{1.5}{v}-\frac{1}{-24}=\frac{1.5-1}{8}$

$⟹v=+72$ cm

Thus distance of image from convex surface is $72$ cm (towards right)

Distance of image from plane surface $d=72-3R=72-3\left(8\right)=48$ cm