Question

Refraction takes place at a convex spherical boundary separating air-glass medium. For the image to be real, the object distance $({\mu }_g=\frac{3}{2})$

• A. Should be greater than two times the radius of curvature of the refracting surface
• B. Should be greater than six times the radius of curvature of the refracting surface
• C. Should be greater than the radius of curvature of the refracting surface
• D. Is independent of the radius of curvature of the refracting surface

Answer 1

The correct option is A Should be greater than two times the radius of curvature of the refracting surface

Applying $\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
$\frac{1.5}{v}-\frac{1}{-u}=\frac{\left(1.5\right)-1}{R}$
Dividing with $1.5$ on both the sides.
or $\frac{1}{v}+\frac{2}{3u}=\frac{1}{3R}$
For v to be positive $\frac{1}{3R}>\frac{2}{3u}$
or $u>2R$