Question

The image for the converging beam after refraction through the curved surface is formed at :

• A. $x=40\text{cm}$
• B. $x=\frac{40}{3}\text{cm}$
• C. $x=-\frac{40}{3}\text{cm}$
• D. $x=\frac{180}{7}\text{cm}$

Answer 1

The correct option is A $x=40\text{cm}$

Using the formula for refraction at spherical surface
$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$
$n_1=\frac{3}{2}$
Here $n_2=1$
$u=30\text{cm}$
$R=+20\text{cm}$
$\frac{1}{v}-\frac{3}{2\times 30}=\frac{1-\frac{3}{2}}{20}$
$v=+40\text{cm}$