Question

A glass dumbbell of length $30$ cm and $\mu =$ 1.5 has ends $3cm$ radius of curvature. An object is situated in air at a distance of $12cm$ from the end of dumb-bell along the axis. The position of image formed due to refraction at one end only is

• A. $16cm$
• B. $18cm$
• C. $20cm$
• D. $24cm$

Answer 1

The correct option is B $18cm$

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{\mu }=\frac{{\mu }_2-{\mu }_1}{R}$

$\frac{1.5}{V}-\frac{1}{12}=\frac{1.5-1}{3}$

$\frac{3}{2V}=\frac{1}{6}+\frac{1}{12}$

$\frac{3}{2V}=\frac{3}{12}$

$V=6cm$

Again, $\frac{{\mu }_2}{V}-\frac{{\mu }_1}{R}$

$\frac{1}{V}-\frac{1.5}{-6}=\frac{-0.5}{-3}$

$\frac{1}{V}=\frac{1}{6}-\frac{3}{12}$ $\Rightarrow$ $V=-12cm$