Chapter 23, Problem 28P

Figure P23.28 shows a curved surface separating a material with index of refraction n₁ from a material with index n₂. The surface forms an image I of object O. The ray shown in red passes through the surface along a radial line. Its angles of incidence and refraction are both zero, so its direction does not change at the surface. For the ray shown in blue, the direction changes according to n₁ sin θ₁ = n₂ sin θ₂. For paraxial rays, we assume θ₁ and θ₂ are small, so we may write n₁ tan θ₁ – n₂ tan θ₂. The magnification is defined as M = h′/h. Prove that the magnification is given by M = –n₁q/n₂p.

Figure P23.28