Question

A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. The focal length of the convex mirror is

• A. 20 cm
• B. 25 cm
• C. 30 cm
• D. 22 cm

Answer 1

Answer: (B)

25 cm

The final image, formed by the combination, is coinciding with the object itself. This implies that the rays, from the object, are retracing their path, after refraction from the lens and reflection from the mirror. The (refracted) rays are, therefore, falling normally on the mirror. Thus the image of the convex lens should form at the center of curvature of the convex mirror.We first find the image distance of the convex lens using the lens formula
$\frac{1}{v}-\frac{1}{(-12)}=\frac{1}{10}$

$\frac{1}{v}=\frac{1}{\left(10\right)}-\frac{1}{12}=\frac{\text{/}2}{\text{/}{120}_{60}}$

$v=60cm$[this is at the centre of curvature of the mirror]

Thus we get the radius of curvature as
$v-d=R$

$60-10=R\Rightarrow R=50cm$

thus we get the focal length as $f=\frac{R}{2}=25cm$