question_answer

Refraction takes place at a concave spherical boundary separating glass air medium. For the image to be real, the object distance \[\left( {{\mu }_{g}}=\frac{3}{2} \right)\]

A) should be greater than three times the radius of curvature of the refracting surface

B) should be greater than two 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

Correct Answer: A

Solution :

Applying, \[\frac{{{\mu }_{2}}}{v}-\frac{{{\mu }_{1}}}{u}=\frac{{{\mu }_{2}}-{{\mu }_{1}}}{R}\]

\[\frac{1}{v}-\frac{1.5}{\left( -5 \right)}=\frac{1-\left( 1.5 \right)}{-R}\] or \[\frac{1}{v}+\frac{3}{2u}=\frac{1}{2R}\]

For v to be positive \[\frac{1}{2R}>\frac{3}{2u}\] or \[u>3R\]