question_answer

Consider a bi-convex lens and a plano-convex lens, with radii of curvature of all the curved surfaces being same. If /is the focal length of bi-convex lens then, the focal length of the plano-convex lens is

A)  \[4f\]   

B)  \[2f\]    

C)  \[f\]      

D)  \[0.5f\]

Correct Answer: B

Solution :

 Consider the type of lenses shown below: For bi-convex lens, focal length is given by \[\frac{1}{{{f}_{b}}}=(\mu -1)\left( \frac{1}{R}+\frac{1}{R} \right)=\frac{2(\mu -1)}{R}\] For plano-convex lens focal length is given by \[\frac{1}{{{f}_{p}}}=(\mu -1)\left( \frac{1}{R}+\frac{1}{R} \right)=\frac{(\mu -1)}{R}\] \[\Rightarrow \]\[\frac{{{f}_{b}}}{{{f}_{p}}}=\frac{\frac{R}{2(\mu -1)}}{\frac{R}{(\mu -1)}}=\frac{1}{2}\Rightarrow {{f}_{p}}=2{{f}_{b}}=2f\]