A biconvex thick lens is made of glass ( = 1.50 ). Both of the surfaces have a radius of 10 cm , and the central thickness is 5 cm . Determine the location of the image for an object situated far away from the lens.

Step-by-step solution

For the first surface, using the formula for refraction at a spherical surface: ₂ v₁ - ₁ u = ₂ - ₁ R₁ Given ₁ = 1 , ₂ = 1.5 , u = - , and R₁ = +10 cm : 1.5 v₁ - 0 = 1.5 - 1 10 1.5 v₁ = 0.5 10 v₁ = 30 cm The image formed by the first surface acts as a virtual object for the second surface. The object distance for the second surface is: u₂ = v₁ - t = 30 - 5 = +25 cm For the second surface, light travels from glass to air. Using ₁ = 1.5 , ₂ = 1 , and R₂ = -10 cm : ₂ v₂ - ₁ u₂ = ₂ - ₁ R₂ 1 v₂ - 1.5 25 = 1 - 1.5 -10 1 v