A parallel beam of light of transverse width 2 mm is incident on a convex lens of focal length 20 cm . A second convex lens is placed coaxially such that the emergent beam is again parallel to the principal axis, but its transverse width becomes 5 mm . The distance between the two lenses is :

Step-by-step solution

Since the incident beam is parallel and the emergent beam is also parallel, the two lenses form an afocal system. This means their principal foci coincide, and the distance between them is d = f₁ + f₂ . The marginal rays of the beam form similar triangles with the principal axis, with their common vertex at the shared focal point. From the properties of similar triangles, the ratio of the transverse beam widths is equal to the ratio of the focal lengths of the respective lenses: w₂ w₁ = f₂ f₁ Substituting the given