A convex lens of focal length 20 cm and a concave lens of focal length 10 cm are placed 10 cm apart with their principal axes coinciding. A beam of light travelling parallel to the principal axis and having a beam diameter of 5.0 mm , is incident on the combination. The emergent beam is parallel to the incident one. Find the possible values for the beam diameter of the emergent beam.

Step-by-step solution

Case I: Light is incident on the convex lens first. The incident parallel beam converges towards the principal focus of the convex lens, which is at a distance of 20 cm from it. The concave lens is placed 10 cm from the convex lens. The distance of the focus of the convex lens from the concave lens is 20 - 10 = 10 cm . This point acts as a virtual object for the concave lens. Since the focal length of the concave lens is 10 cm , the emergent beam becomes parallel to the principal axis. Using similar triangles, the