Question

Two spherical mirrors (convex and concave ) having the same focal length of 36 cm are arranged as shown in figure so that their optical axes coincide. The separation between the mirrors in 1 m. At what distance from the concave mirror should an object be placed so that its images formed by the concave and convex mirrors independently are identical in size?

Answer 1

Let the object be placed at a distance 'u' from concave mirror.

The reflection will be at a distance

$\frac{uf}{u-f}$

Magnification will be given as :

$-\frac{uf}{u-f}/u=\frac{f}{u-f}$

Magnification for convex mirror will be given by:

$-\frac{f}{l-u+f}$

where,

l is the separation between the two mirrors.

Equating the magnification by concave and convex mirror,

$\frac{f}{u-f}=\frac{f}{l-u+f}$

Solving the equation,

$u=\frac{l}{2}+f$

$u=\frac{100}{2}+36cm$

$u=86cm$