Question

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

Answer 1

Hint: A concave lens is a lens that has at least one curved surface inwards. When a light ray is projected on this lens the rays which refract through the curved surface spread out; hence it is a diverging lens.

Complete step by step answer:
Given that a point object is at a distance of 20cm on the axis and its image is coinciding with itself hence we can say the image formed is at the point of object O.

Since the image I of the object O is at the same point so we can say that the ray first refracted from the convex lens and refracted from the plane mirror must be retracing their path. This retracing is possible when the ray refracted from the convex lens must fall normally to the surface of the mirror, that is the ray is parallel to the principal axis.
As angle of incidence is equal to the angle of reflection and if angle of incidence is at zero degree then angle of reflection will become 0 degree therefore the retracing path of the ray becomes the same.
Hence we can say the object must be at the focus of convex lens where \[f = CO = 20cm\]

Note:In convex lens when an object is kept as focus then the ray of light after refraction from lens becomes parallel to the principal axis and this length of object from lens is called focal length of lens.