Question

A plano-convex lens of refractive index $1.5$ and radius of curvature $30cm$ is silvered at the curved surface. Now this lens has to be formed to form the image of an object. At what distance from this lens, an object is to be placed in order to have a real image of the size of the object?

• A. $20cm$
• B. $30cm$
• C. $60cm$
• D. $80cm$

Answer 1

The correct option is A $20cm$

Given: A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now this lens has to be formed to form the image of an object.

To find the distance from this lens, an object is to be placed in order to have a real image of the size of the object

Solution:

As per given criteria,

${\mu }_{plano-convex}=1.5$

Radius of curvature, $R=30cm$

Therefore the focal length becomes, $f=\frac{R}{2\mu }=\frac{30}{2\times 1.5}=10cm$

Therefore the distance of the object, to form an image of object size,

the object should be placed at $2\times$ focal length of the concave mirror,

So the required distance of the object from the lens = $2\times f=2\times 10=20cm$