Two thin lenses are placed in contact such that the equivalent focal length of the combination is +50 cm . If one of the lenses is a convex lens of focal length 20 cm , what is the focal length and nature of the second lens?

Step-by-step solution

Let the equivalent focal length of the combination be F_ eq and the focal lengths of the individual lenses be f₁ and f₂ . Given: F_ eq = +50 cm f₁ = +20 cm (since it is a convex lens) The formula for the equivalent focal length of thin lenses in contact is: 1 F_ eq = 1 f₁ + 1 f₂ Substituting the given values: 1 50 = 1 20 + 1 f₂ 1 f₂ = 1 50 - 1 20 1 f₂ = 2 - 5 100 = - 3 100 cm ⁻¹ f₂ = - 100 3 cm The negative sign indicates that the second lens is a concave lens. Therefore, it is a concave lens of focal length 100 3