Question

In the given setup, consider the case where the first image formed by the plane mirror is taken as an object for the concave mirror. Which of the following can be the correct distance of the image formed by the concave mirror from the pole?

• A. $30\text{cm}$
• B. $20\text{cm}$
• C. $50\text{cm}$
• D. $10\text{cm}$

Answer 1

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


Given:
The original object is kept at the center of curvature of concave mirror, which is at 40 cm from the pole.

Since focal length is half the radius of curvature, focus is at 20 cm from the pole.

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 is 60 cm. In other words, the object for the mirror is placed at beyond C. And when for a concave mirror object is placed beyond C, the image will formed between C and F.
Object distance will satisfy $20cm<|u|<40cm$

This result can also be verified using the mirror formula.

The only option satisfying this criteria is 30 cm..