Question

Find out the distance of the image formed by the concave mirror from the pole, if the first image formed by the plane mirror is taken as an object for the given concave mirror.

• A. $20\text{cm}$
• B. $60\text{cm}$
• C. $40\text{cm}$
• D. $30\text{cm}$

Answer 1

The correct option is D $30\text{cm}$

Given:
The original object is kept at the center of curvature of concave mirror.
Focal length of concave mirror taking the right side as positive and left as negative:
$f=-20\text{cm}$

Distance between the plane mirror and concave mirror, $d=50\text{cm}$

For plane mirror, image distance equals the object distance.
Hence, distance of the image of plane mirror from the pole of the concave mirror is $50+10=60\text{cm}$

This image acts as object for concave mirror.
So, object distance for concave mirror:
$u=-60\text{cm}$

Let the image distance be $v$
Applying mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-60}=\frac{1}{-20}$
$v=-30$

Thus the final image is formed at a distance of $30\text{cm}$ to the left when measured from the pole of the concave mirror.