Question

An object is placed at a distance of $2f$ from a concave mirror. Light reflected from the mirror falls on a plane mirror. The distance of the plane mirror from the concave mirror equals $f$. The distance of the final image from the concave mirror (due to reflection at both concave and plane mirror) is :

• A. $f$
• B. $\frac{f}{2}$
• C. $2f$
• D. Zero

Answer 1

Answer: (D)

Zero

For a concave mirror, when object is at 2f. image is formed at 2f.
Hence, $v_1=-2f$ for concave mirror
Image formed by concave mirror serves as an object to plane mirror.
Position of plane mirror with respect to concave mirror is $d=-f$

Hence, position of object for plane mirror is, $u_2=-f$, (origin shifted to left)
Hence, position of image for plane mirror is, $v_2=+f$
Position of final image wrt the concave mirror is $v_3=v_2+d=0$, (origin shifted to right)