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

Hint:A convex lens is also known as a converging lens. That is, it converges the rays of light to the point known as the focus. The focal length is nothing but the distance from the lens to the focus where the light converges. However, the image formation shows variation due to the presence of the plane mirror. Hence, we have to study the question and perform the calculations accordingly.

Complete answer:

is kept at a distance of 20cm on the axis. The image coincides with itself. Consider the line OC in the figure. Its distance is 20cm.Since the image coincides with the object we can say that the rays are initially refracted by the lens and further refracted by the mirror and the path gets retraced. This occurs when the rays are normally incident on the mirror, by forming beams that are parallel to the principal axis of the lens. This phenomenon occurs when the image is kept at the focal length of the lens.

Thus the value of the focal length of the lens is 20cm.

Note:In the case of mirrors, the image formed coincides with the object when it is placed at the centre of curvature. However it is distinct as an inverted image is formed. When an object is kept at the focal length in mirrors, the image is formed at infinity.