MASSACHUSETTS INSTITUTE OF TECHNOLOGY2.710 Optics Fall ’05Problem Set #2 Posted Sept. 14, 2005 — Due Wednesday, Sept. 21, 20051. The spoon Compare the image of yourself that you observe looking at the convexsurface of a spoon with the image from a flat mirror. Do some simple raytracingto explain the difference.2. Wanda’s world Your goldfish Wanda lives in a sphere of water (refractive indexn = 1.3, radius |R| = 20cm). At one instance, Wanda has wandered to the centerof here water world (see Fig. 2 below). Model Wanda as a stick perpendicular tothe optical axis and the water sphere as a thick lens. You may ignore the effectof the glass container of Wanda’s worlda) Where is Wanda’s image formed?b) Is the image erect or inverted?c) What is the magnification?|waterWandaairR|Figure 2: Wanda’s worldRain DropsWindshieldFigure 33. Design an optical system which can detect the amount of water present on a car’swindshield to adjust the wiper speed.Hint: indices of refraction nglass= 1.5, nwater= 1.33, nair= 1.0.incomingrays1nfsxzFigure 44. Lens-in-a-pool Consider a perfectly focussing one-dimensional paraboloid mir-ror filled with a fluid of refractive index n. The mirror surface is described bythe equation s(x) = x2/4f, where f is the focal length of the mirror. The fluidis present up to a height of f. Light is incident from the top as shown in Figure4. You may neglect the slight reflection that occurs when the light rays go fromthe air into the fluid.a) Calculate the portion of the incoming ray bundle which will exit from thefluid as a divergent ray bundle after focusing.2b) Show that the remaining rays will exit as a parallel ray bundle.c) Suppose that the incoming ray bundle is shadowed by the letter “A.” If youplaced a camera just above the focal point (in air), what would you observe?You need not write any equations, just reason
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