An object is placed at a distance of 20 cm in front of a combination of two thin lenses in contact. A real image is formed at a distance of 30 cm from the combination. The first lens is equiconvex with a refractive index of 1.5 and a radius of curvature of 30 cm for both surfaces. If the second lens is plano-convex with a radius of curvature of 12 cm for its curved surface, what is the refractive index of the materia

Step-by-step solution

Using the thin lens formula for the combination to find its equivalent focal length F : 1 v - 1 u = 1 F 1 +30 - 1 -20 = 1 F 1 F = 1 30 + 1 20 = 5 60 = 1 12 cm ⁻¹ Using the lens maker's formula to find the focal length of the first equiconvex lens f₁ : 1 f₁ = ( ₁ - 1) ( 1 R₁ - 1 -R₁ ) 1 f₁ = (1.5 - 1) ( 2 30 ) = 0.5 1 15 = 1 30 cm ⁻¹ The equivalent focal length of two thin lenses in contact is given by: 1 F = 1 f₁ + 1 f₂ 1 12 = 1 30 + 1 f₂ 1 f₂ = 1 12 - 1 30 = 5 - 2 60 = 3 60 = 1 20 cm ⁻¹ Using the lens maker's form