Question

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

1. 20 cm
2.25cm
3.15cm
4.30cm

the answer is option 2 . I need the explanation part . can anyone explain .​

Answer 1

Answer:

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

v

1

−

(−12)

1

=

10

1

v

1

=

(10)

1

−

12

1

=



120

60



2

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⇒R=50cm

thus we get the focal length as f=

2

R

=25cm