A composite biconvex lens is made by placing two thin plano-convex lenses with their plane surfaces in contact. The left plano-convex lens has a refractive index of 1.6 and a radius of curvature of 10 cm for its curved surface. The right plano-convex lens has a radius of curvature of 20 cm for its curved surface, but its refractive index ₂ is unknown. When an object is placed at a distance of 15 cm to the left of the

Step-by-step solution

For a real image, the magnification is negative, so m = -2 . Using the magnification formula for a lens, m = v u : -2 = v -15 v = +30 cm. Applying the lens formula to find the equivalent focal length F of the combination : 1 v - 1 u = 1 F 1 30 - 1 -15 = 1 F 1 F = 1 30 + 2 30 = 3 30 = 1 10 cm ⁻¹ . The equivalent power of the composite lens is P = 1 F = 0.10 cm ⁻¹ . Using the lens maker's formula, the power of the left plano-convex lens is : P₁ = ( ₁ - 1) ( 1 R₁ ) = (1.6 - 1) ( 1 10 ) = 0.6 10 = 0.06 cm ⁻¹ . The powe