Question

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

Answer 1

Answer: (B)

Consider the type of lenses shown below:
For bi- Plano 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
$\frac{1}{f_b}=(\mu -1)\left(\frac{1}{R}+\frac{1}{R}\right)$
$=\frac{(\mu -1)}{R}$
$\Rightarrow \frac{f_b}{f_p}=\frac{\frac{R}{2(\mu -1)}}{\frac{R}{(\mu -1)}}$
$=\frac{1=2f_b}{2}$
$\Rightarrow f_p=2f$