A plano-convex glass (n = 1.5) lens has a curved side whose radius is 50 cm. If the image size is to be the same as the object size, the object should be placed at a distance from the lens of:
A) 50 cm
B) 100 cm
C) 200 cm
D) 400 cm
E) 340 cm

Question

Quizplus · Accepted Answer

Assuming the lens formula: $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$, where $f$ is the focal length of the lens, $v$ is the image distance and $u$ is the object distance.

From the given information, the radius of curvature ($R$) of the lens is 50 cm. Therefore, the focal length of the lens will be:

$f=\frac{n-1}{R}$
$f=\frac{1.5-1}{50cm}$
$f=0.01m$

Now, as per the question, the image size needs to be the same as the object size, which means the magnification will be 1.

$m=\frac{v}{u}=1$

Therefore, $v=u$

Substituting these values in the lens formula, we get:

$\frac{1}{0.01}=\frac{1}{u}-\frac{1}{u}$

$u=0.01m$

$u=100cm$

So, the object should be placed at a distance of 100cm from the lens, which is equivalent to choice letter C.

A Plano-Convex Glass (N = 1