Task id12106

For a thick glass lens with radii of curvature r1 and r2 and thickness d (Fig. 14.31), located in air, the focal length F is determined by the following expression: F = nr1r2 where n is the refractive index (air - glass). Note: ri > 0 means that the center of curvature Oi lies on the right side of the point Si; ri < 0 means that the center of curvature Oi lies on the left side of the point Si (i=1, 2). For certain purposes, it is desirable that the focal length does not depend on the wavelength of light λ. Complete the following tasks and answer the questions: 1. For how many different wavelengths can the same focal length be achieved? 2. Find the relationship between ri, d and the refractive indices such that the focal length of the lens is independent of the wavelength of light (see previous question) and discuss this relationship. Draw possible lens shapes. Indicate the positions of the centers of curvature O1 and O2. 3. Show that for a plano-convex lens, a specific focal length can be obtained for only one wavelength of light. 4. Indicate other cases when, with certain parameters of a thick lens, it is possible to realize a given focal length for only one wavelength.