Question

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

• A. 20 cm, from the pole
• B. 30 cm, from the pole
• C. 40 cm, from the pole
• D. 60 cm, from the pole

Answer 1

The correct option is B

30 cm, from the pole

Given:
Original object is kept at the center of curvature of concave mirror.
Focal length of concave mirror taking right direction as positive:
$f=-20cm$
Distance between the plane mirror and concave mirror, $d=50cm$

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 $50+10=60cm$

This image acts as object for concave mirror.
So, object distance for concave mirror:
$u=-60cm$
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 $30cm$, in the left direction from the pole of the concave mirror.