Simple Nature - Light and Matter

33 The figure shows four lenses. Lens 1 has two spherical surfaces.Lens 2 is the same as lens 1 but turned around. Lens 3 ismade by cutting through lens 1 and turning the bottom around.Lens 4 is made by cutting a central circle out of lens 1 and recessingit.(a) A parallel beam of light enters lens 1 from the left, parallelto its axis. Reasoning based on Snell’s law, will the beam emergingfrom the lens be bent inward, or outward, or will it remain parallelto the axis? Explain your reasoning. As part of your answer, makea huge drawing of one small part of the lens, and apply Snell’s lawat both interfaces. Recall that rays are bent more if they come tothe interface at a larger angle with respect to the normal.(b) What will happen with lenses 2, 3, and 4? Explain. Drawingsare not necessary.34 The drawing shows the anatomy of the human eye, at twicelife size. Find the radius of curvature of the outer surface of thecornea by measurements on the figure, and then derive the focallength of the air-cornea interface, where almost all the focusing oflight occurs. You will need to use physical reasoning to modifythe lensmaker’s equation for the case where there is only a singlerefracting surface. Assume that the index of refraction of the corneais essentially that of water.35 An object is less than one focal length from a converging lens.(a) Draw a ray diagram. (b) Using reasoning like that developedin section 12.3, determine the positive and negative signs in theequation 1/f = ±1/d i ± 1/d o . (c) The images of the rose in section4.2 were made using a lens with a focal length of 23 cm. If the lens√is placed 10 cm from the rose, locate the image.36 Nearsighted people wear glasses whose lenses are diverging.(a) Draw a ray diagram. For simplicity pretend that there is noeye behind the glasses. (b) Using reasoning like that developedin section 12.3, determine the positive and negative signs in theequation 1/f = ±1/d i ± 1/d o . (c) If the focal length of the lens is50.0 cm, and the person is looking at an object at a distance of 80.0√cm, locate the image.37 (a) Light is being reflected diffusely from an object 1.000 munderwater. The light that comes up to the surface is refracted atthe water-air interface. If the refracted rays all appear to come fromthe same point, then there will be a virtual image of the object inthe water, above the object’s actual position, which will be visibleto an observer above the water. Consider three rays, A, B and C,whose angles in the water with respect to the normal are θ i = 0.000 ◦ ,1.000 ◦ and 20.000 ◦ respectively. Find the depth of the point at whichthe refracted parts of A and B appear to have intersected, and dothe same for A and C. Show that the intersections are at nearly theProblem 33.Problem 34.Problems 801