A point object is positioned at a distance of 15 cm from a convex lens. The image forms on the opposite side at a distance of 30 cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts further away by 30 cm . Determine the focal lengths of the two lenses.

Step-by-step solution

For the convex lens, the object distance is u = -15 cm and the image distance is v = +30 cm . Using the lens formula 1 v - 1 u = 1 f₁ : 1 30 - 1 -15 = 1 f₁ 1 f₁ = 1 30 + 2 30 = 3 30 = 1 10 f₁ = 10 cm When the concave lens is placed in contact, the image shifts further away by 30 cm . The new image distance is v' = 30 + 30 = +60 cm . Using the lens formula for the combination: 1 v' - 1 u = 1 F 1 60 - 1 -15 = 1 F 1 F = 1 60 + 4 60 = 5 60 = 1 12 F = 12 cm The equivalent focal length of two thin lenses in contact is gi