Question

At what distance from $O$ the image for the converging beam after refraction through the curved surface will be formed?

• A. $40\text{cm}$
• B. $\frac{40}{3}\text{cm}$
• C. $20\text{cm}$
• D. $\frac{180}{7}\text{cm}$

Answer 1

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

Given that,
Refractive index of surrounding, ${\mu }_1=\frac{3}{2}$
Refractive index of lens, ${\mu }_2=1$
Radius of curvature of the lens, $R=20\text{cm}$

Sign convention: Direction along incident ray is taken as +ve.

Using the formula for refraction through a curved surface.
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\frac{1}{v}-\frac{\frac{3}{2}}{30}=\frac{1-\frac{3}{2}}{20}$

$\Rightarrow v=40\text{cm}$


$\begin{array}{c}\text{Why this question}?\\ \text{This question checks the basic understanding of}\\ \text{application of the formula of law of refraction on}\\ \text{curved surface, and the concept of virtual object.}\\ \text{Caution : Use the sign-convention carefully.}\end{array}$