Question

A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?

Answer 1

Figure shows a convex lens placed in contact with a plane mirror. An axial point object is placed at a distance O at a distance,
OC = 20cm.

As the image I of the object coincides with O, the rays refracted first from the lens and then refracted by the plane mirror must be retracing their path. This would happen when rays refracted by the convex lens fall normally on the mirror I.e, the refracted rays form a beam parallel to principal axis of the lens. Hence the object O must be at the focus of the convex lens.
f = CO = 20 cm.

Answer 2

Answer:

focal length= 20cm

here for condition that image and object coincide rays should retrace the path..

for that rays should be incident normally..

i.e. they should be parallel to each other.. for that they should come from infinity..

i.e. convex lens have to produce image at infinity..

for that object should be kept at focus of convex lens..

so that object distance= focal length= 20cm

thank you