A composite biconvex lens is formed by placing two thin plano-convex lenses with their plane surfaces in contact. The left plano-convex lens has a refractive index of 1.5 and a radius of curvature of 20 cm. The right plano-convex lens has a refractive index of 1.6 and a radius of curvature of 16 cm. The curved surface of the right lens is silvered. If an object is placed at a distance of 12 cm to the left of this opt

Step-by-step solution

The system acts as an equivalent mirror. First, we find the equivalent power of the unsilvered composite lens P_L . Power of the left plano-convex lens : P₁ = ( ₁ - 1) ( 1 R₁ ) = (1.5 - 1) ( 1 20 ) = 0.5 20 = 1 40 cm ⁻¹ . Power of the right plano-convex lens (unsilvered) : P₂ = ( ₂ - 1) ( 1 R₂ ) = (1.6 - 1) ( 1 16 ) = 0.6 16 = 3 80 cm ⁻¹ . Equivalent power of the lens combination : P_L = P₁ + P₂ = 1 40 + 3 80 = 5 80 = 1 16 cm ⁻¹ . The silvered curved surface of the right lens acts as a concave mirror with radius R