Question

The radius of curvature of the curved surface of a plano-convex lens is $20cm$. If the refractive index of the material of the lens be $1.5$, it will

• A. act as a convex lens only for the objects that lie on its curved side
• B. act as a concave lens for the objects that lie on its curved side
• C. act as a convex lens irrespective of the side on which the object lies
• D. act as a concave lens irrespective of side on which the object lies

Answer 1

Answer: (C)

Here, $\mu =1.5$
If object lies on plane side;
$R_1=\infty ,R_2=-20cm$

$\frac{1}{f}=\left(\mu -1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
$=\left(1.5-1\right)\left(\frac{1}{\infty }+\frac{1}{20}\right)=\frac{1}{40}$
$f=+40cm$. The lens behaves as convex lens.
If object lies on its curved side. Then
$R_1=20cm,R_2=\infty$

$\frac{1}{f^{\prime }}=\left(\mu -1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
$=\left(1.5-1\right)\left(\frac{1}{20}-\frac{1}{\infty }\right)=\frac{1}{40}$
$f^{\prime }=40cm$.
The lens behaves as convex lens.