Question

An object is placed in front of a converging lens at a distance equal to twice the focal length $f_1$ of the lens. On the other side of the lens is a concave mirror of focal length $f_2$ separated from the lens by a distance $2(f_1+f_2)$. Light from the object passes rightward through the lens, reflects from the mirror, passes leftward through the lens, and forms a final image of the object.

• A. The distance between the lens and the final image is equal to $2f_1$
• B. The distance between the lens and the final image is equal to $2(f_1+f_2)$
• C. The final image is real, inverted and of same size as that of the object
• D. The final image is real, erect and of same size as that of the object

Answer 1

Answer: (A), (C)

The distance between the lens and the final image is equal to $2f_1$
The final image is real, inverted and of same size as that of the object

As the image formed by the lens is at $v=+2f_1$
$m_1=\frac{v}{u}=-1$
This serves as object for the mirror placed at the center of the mirrror. So final image would form again at the same place .
$m_2=\frac{-v}{u}=-1$
this again serves as object for lens , image is formed at $2f_1$ to the left of lens
$m_3=-1$
Total magnification is $m=m_1{m}_2{m}_3=-1$
Final image is real and inverted
Option $A,C$ are correct