Question

Find the position of image ?

• A. $+20\text{cm}$
• B. $+45\text{cm}$
• C. $-45\text{cm}$
• D. $+30\text{cm}$

Answer 1

The correct option is B $+45\text{cm}$


Given,
${\mu }_1=1$ and ${\mu }_2=1.5$

Radius of curvature, $R=6\text{cm}$

Object distance, $u=-20\text{cm}$

Using relation between object and image distance for refraction at curved surfaces, $$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$$Substituting the values,

$\Rightarrow \frac{1.5}{v}-\frac{1}{(-20)}=\frac{1.5-1}{+6}$

$\Rightarrow \frac{1.5}{v}=\frac{1}{12}-\frac{1}{20}$

$\Rightarrow v=\left(\frac{12\times 20}{20-12}\right)\times 1.5$

$\therefore v=45\text{cm}$

Hence, option (b) is the correct answer.

$$\begin{array}{c}\text{Why this question:}\\ \text{To understand the relation between image distance \& object distance}\\ \text{when refraction occurs through curved surfaces.}\end{array}$$