question_answer

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

A) \[4\,f\]    

B) \[2\,f\]

C) \[f\]   

D) \[0.5\,\,f\,\]

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 \[\frac{1}{{{f}_{b}}}=(\mu -1)\,\,\left( \frac{1}{R}+\frac{1}{R} \right)=\frac{(\mu -1)}{R}\] \[\Rightarrow \] \[\frac{{{f}_{b}}}{{{f}_{p}}}=\frac{\frac{R}{2(\mu -1)}}{\frac{R}{(\mu -1)}}=\frac{1=2\,{{f}_{b}}}{2}\Rightarrow {{f}_{p}}=2f\]