Conceptual Questions

ssm Solution is in the Student Solutions Manual

| 1 | Suppose that a radio station broadcasts simultaneously from two transmitting antennas at two different locations. Is it clear that your radio will have better reception with two transmitting antennas rather than one? Justify your answer.

| 2 | Two sources of waves are in phase and produce identical waves. These sources are mounted at the corners of a square. At the center of the square waves from the sources produce constructive interference, no matter which two corners of the square are occupied by the sources. Explain why.

| 3 | ssm (a) How would the pattern of bright and dark fringes produced in a Young’s double-slit experiment change if the light waves coming from both slits had their phases shifted by an amount equivalent to a half wavelength? (b) How would the pattern change if the light coming from only one of the slits had its phase shifted by an amount equivalent to a half wavelength?

| 4 | Replace slits S1 and S2 in Figure 27-4 with identical in-phase loudspeakers and use the same ac electrical signal to drive them.The two sound waves produced will then be identical, and you will have the audio equivalent of Young’s double-slit experiment. In terms of loudness and softness, describe what you would hear as you walked along the screen, starting from the center and going to either end.

| 5 | In Young’s double-slit experiment, is it possible to see interference fringes when the wavelength of the light is greater than the distance between the slits? Provide a reason for your answer.

| 6 | A camera lens is covered with a nonreflective coating that eliminates the reflection of perpendicularly incident green light. Recalling Snell’s law of refraction (see Section 26.2), would you expect the reflected green light to be eliminated if it were incident on the nonreflective coating at an angle of 45° rather than perpendicularly? Justify your answer.

| 7 | When sunlight reflects from a thin film of soapy water, the film appears multicolored, in part because destructive interference removes different wavelengths from the light reflected at different places, depending on the thickness of the film. As the film becomes thinner and thinner, it looks darker and darker in reflected light, appearing black just before it breaks. The blackness means that destructive interference removes all wavelengths from the reflected light when the film is very thin. Explain why.

| 8 | Two pieces of the same glass are covered with thin films of different materials. The thickness of each film is the same. In reflected sunlight, however, the films have different colors. Give a reason that accounts for the difference in colors.

| 9 | In Figure 27-14b there is a dark spot at the center of the pattern of Newton’s rings. By considering the phase changes that occur when light reflects from the upper curved surface and the lower flat surface, account for the dark spot.

| 10 | ssm A thin film of a material is floating on water (n = 1.33). When the material has a refractive index of n = 1.20, the film looks bright in reflected light as its thickness approaches zero. But when the material has a refractive index of n = 1.45, the film looks black in reflected light as its thickness approaches zero. Explain these observations in terms of constructive and destructive interference and the phase changes that occur when light waves undergo reflection.

| 11 | A transparent coating is deposited on a glass plate and has a refractive index that is larger than that of the glass, not smaller, as it is for a typical nonreflective coating. For a certain wavelength within the coating, the thickness of the coating is a quarter wavelength. The coating enhances the reflection of the light corresponding to this wavelength. Explain why, referring to Example 3 in the text to guide your thinking.

| 12 | On most cameras one can select the f-number setting, or f-stop. The f-number gives the ratio of the focal length of the camera lens to the diameter of the aperture through which light enters the camera. If one wishes to resolve two closely spaced objects in a picture, should a small or a large f-number setting be used? Account for your answer.

| 13 | Explain why a sound wave diffracts much more than a light wave does when the two pass through the same doorway.

| 14 | Review Conceptual Example 8 before answering this question. A person is viewing one of Seurat’s paintings that consists of dots of color. She is so close to the painting that the dots are distinguishable. Without moving, however, she can squint, which makes the painting take on a more normal appearance. In terms of the Rayleigh criterion, why does squinting make the painting look more normal?

| 15 | Four light bulbs are arranged at the corners of a rectangle that is three times longer than it is wide. You look at this arrangement perpendicular to the plane of the rectangle. From very far away, your eyes cannot resolve the individual bulbs and you see a single smear of light. From close in, you see the individual bulbs. Between these two extremes, what do you see? Draw two pictures to illustrate the possibilities that exist, depending on how far away you are. Explain your drawings.

| 16 | Suppose the pupil of your eye were elliptical instead of circular in shape, with the long axis of the ellipse oriented in the vertical direction. (a) Would the resolving power of your eye be the same in the horizontal and vertical directions? (b) In which direction would the resolving power be greatest? Justify your answers by discussing how the diffraction of light waves would differ in the two directions.

| 17 | ssm Suppose you were designing an eye and could select the size of the pupil and the wavelengths of the electromagnetic waves to which the eye is sensitive. As far as the limitation created by diffraction is concerned, rank the following design choices in order of decreasing resolving power (greatest first): (a) large pupil and ultraviolet wavelengths, (b) small pupil and infrared wavelengths, and (c) small pupil and ultraviolet wavelengths. Justify your answer.

| 18 | In our discussion of single-slit diffraction, we considered the ratio of the wavelength to the width W of the slit. We ignored the height of the slit, in effect assuming that the height was much larger than the width. Suppose the height and width were the same size, so that diffraction in both dimensions occurred. How would the diffraction pattern in Figure 27-19b be altered? Give your reasoning.

| 19 | What would happen to the distance between the bright fringes produced by a diffraction grating if the entire interference apparatus (light source, grating, and screen) were immersed in water? Why?

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