Figure P36.34 shows a curved surface separating a material

Chapter 36, Problem 34

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Figure P36.34 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 Snells law, n1 sin u1 5 n2 sin u2. For paraxial rays, we assume u1 and u2 are small, so we may write n1 tan u1 5 n2 tan u2. The magnification is defined as M 5 h9/h. Prove that the magnification is given by M 5 2n1q/n2p