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# The lens shown in FIGURE CP35.49 is called an achromatic ISBN: 9780134081496 191

## Solution for problem 35.78 Chapter 35

Physics for Scientists and Engineers: A Strategic Approach, Standard Edition (Chs 1-36) | 4th Edition

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Problem 35.78

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/12n2 - n1 - 12, where n1 and n2 are, respectively, the indices of refraction of the diverging and the converging lenses. Dont 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 n1 and n2 as nblue - nred for the two lenses. What value of the ratio n1 /n2 makes fblue = fred 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. nblue nred Crown glass 1.525 1.517 Flint glass 1.632 1.616 d. What value of R gives a focal length of 10.0 cm?

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##### ISBN: 9780134081496

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