The lens shown in FIGURE CP35.49 is called an achromatic doublet, meaning that it has no chromatic aberration. The left side is flat, and all other surfaces have radii of curvature R.

a. For parallel light rays coming from the left, show that the effective focal length of this two-lens system is f = R/(2n₂ - n₁ - 1), where n₁ and n₂ are, respectively, the indices of refraction of the diverging and the converging lenses. Don??t forget to make the thin-lens approximation.b. Because of dispersion, either lens alone would focus red rays and blue rays at different points. Define Δn₁ and Δn₂ as n_blue - n_red for the two lenses. What value of the ratio Δn₁ /Δn₂ makes f_blue = f_red for the two-lens system? That is, the two-lens system does not exhibit chromatic aberration.c. Indices of refraction for two types of glass are given in the table. To make an achromatic doublet, which glass should you use for the converging lens and which for the diverging lens? Explain.

d. What value of R gives a focal length of 10.0 cm?

FIGURE CP35.49