Solved: The wavelength of the laser beam used in a compact

Two separate coherent sources produce waves whose wavelengths are 0.10 m. The two waves spread out and overlap at a certain point. Does constructive or destructive interference occur at this point when (a) one wave travels 3.20 m and the other travels 3.00 m, (b) one wave travels 3.20 m and the other travels 3.05 m, (c) one wave travels 3.20 m and the other travels 2.95 m?

Suppose that a radio station broadcasts simultaneously from two transmitting antennas at two different locations. Compared with only one transmitting antenna, the reception with two transmitting antennas (a) is always better (b) is always worse (c) can be either better or worse, depending on the distance traveled by each wave.

Two sources of waves are in phase and produce identical waves. These sources are mounted at the corners of a square and broadcast waves uniformly in all directions. At the center of the square, will the waves always produce constructive interference no matter which two corners of the square are occupied by the sources?

Red light ( 664 nm in vacuum) is used in Youngs experiment with the slits separated by a distance d 1.20  104 m. The screen in Figure 27.7 is located at a distance of L 2.75 m from the slits. Find the distance y on the screen between the central bright fringe and the thirdorder bright fringe. Reas

Figure 27.8 shows a photograph that illustrates the kind of interference fringes that can result when white light, which is a mixture of all colors, is used in Youngs experiment. Except for the central fringe, which is white, the bright fringes are a rainbow of colors. Why does Youngs experiment separate white light into its constituent colors? In any group of colored fringes, such as the two singled out in Figure 27.8, why is red farther out from the central fringe than green is? And finally, why is the central fringe white rather than colored?

Replace the slits S1 and S2 in Figure 27.3 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 Youngs double-slit experiment. In terms of loudness and softness, what would you hear as you walk along the screen, starting from the center and going to either end? (a) Loud, then soft, then loud, then soft, etc., with the loud sounds decreasing in intensity as you walk away from the center (b) Loud, then soft, then loud, then soft, etc., with the loud sounds increasing in intensity as you walk away from the center (c) Soft, then loud, then soft, then loud, etc., with the loud sounds decreasing in intensity as you walk away from the center (d) Soft, then loud, then soft, then loud, etc., with the loud sounds increasing in intensity as you walk away from the center

The drawing shows two double slits that have slit separations of d1 and d2. Light whose wavelength is either 1 or 2 passes through the slits. For comparison, the wavelengths are also illustrated in the drawing. For which combination of slit separation and wavelength would the pattern of bright and dark fringes on the observation screen be (a) the most spread out and (b) the least spread out?

Suppose the light waves coming from both slits in a Youngs double-slit experiment had their phases shifted by an amount equivalent to a half-wavelength. (a) Would the pattern be the same or would the positions of the light and dark fringes be interchanged? (b) Would the pattern be the same or would the positions of the light and dark fringes be interchanged if the light coming from only one of the slits had its phase shifted by an amount equivalent to a half-wavelength?

In Youngs double-slit experiment, is it possible to see interference fringes when the wavelength of the light is greater than the distance between the slits?

A thin film of gasoline floats on a puddle of water. Sunlight falls almost perpendicularly on the film and reflects into your eyes. Although sunlight is white since it contains all colors, the film looks yellow because destructive interference eliminates the color of blue (vacuum 469 nm) from the reflected light. The refractive indices of the blue light in gasoline and in water are 1.40 and 1.33, respectively. Determine the minimum nonzero thickness t of the film. R

Under natural conditions, thin films, like gasoline on water or like the soap bubble in Figure 27.11, have a multicolored appearance that often changes while you are watching them. Why are such films multicolored, and what can be inferred from the fact that the colors change in time?

(a) Assuming that green light (vacuum 552 nm) strikes the glass plates nearly perpendicularly in Figure 27.12, determine the number of bright fringes that occur between the place where the plates touch and the edge of the sheet of paper (

A camera lens is covered with a nonreflective coating that eliminates the reflection of perpendicularly incident green light. Recalling Snells 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? (a) No, because the distance traveled by the light in the film is less than twice the film thickness. (b) No, because the distance traveled by the light in the film is greater than twice the film thickness. (c) Yes, the green light will still be eliminated.

Two pieces of the same glass are covered with thin films of different materials. In reflected sunlight, however, the films have different colors. Why? (a) The films could have the same thickness, but different refractive indices. (b) The films could have different thicknesses, but the same refractive indices. (c) Both of the preceding answers could be correct

A transparent coating is deposited on a glass plate and has a refractive index that is larger than that of the glass. For a certain wavelength within the coating, the thickness of the coating is a quarter-wavelength. Does the coating enhance or reduce the reflection of the light corresponding to this wavelength?

The drawings show three situationsA, B, and Cin which light reflects almost perpendicularly from the top and bottom surfaces of a thin film, with the indices of refraction as shown. (a) For which situation(s) will there be a net phase shift (due to reflection) between waves 1 and 2 that is equivalent to either zero wavelengths or one wavelength (film), where film is the wavelength of the light in the film? (b) For which situation(s) will the film appear dark when the thickness of the film is equal to film? 1

When sunlight reflects from a thin film of soapy water (air on both sides), 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. What happens as the film becomes thinner and thinner? (a) Nothing happens, and the film remains multicolored. (b) The film looks brighter and brighter in reflected light, appearing totally white just before it breaks. (c) The film looks darker and darker in reflected light, appearing black just before it breaks.

Two thin films are floating on water (n 1.33). The films have refractive indices of n1 1.20 and n2 1.45. Suppose that the thickness of each film approaches zero. In reflected light, film 1 will look ____ and film 2 will look ____. (a) bright, bright (b) bright, dark (c) dark, bright (d) dark, dark 1

Light passes through a slit and shines on a flat screen that is located L 0.40 m away (see Figure 27.23). The wavelength of the light in a vacuum is 410 nm. The distance between the midpoint of the central bright fringe and the first dark fringe is y. Determine the width 2y of the central bright fringe when the width of the slit is (a) W 5.0 106 m and (b) W 2.5 106 m. Reason

A diffraction pattern is produced on a viewing screen by using a single slit with blue light. Does the pattern broaden or contract (become narrower) (a) when the blue light is replaced by red light (b) when the slit width is increased?

A sound wave has a much greater wavelength than does a light wave. When the two waves pass through a doorway, which one, if either, diffracts to a greater extent? (a) The sound wave (b) The light wave (c) Both waves diffract by the same amount.

(a) A hang glider is flying at an altitude of 120 m. Green light (wavelength 555 nm in vacuum) enters the pilots eye through a pupil that has a diameter of 2.5 mm. Determine how far apart two point objects must be on the ground if the pilot is to have any hope of distinguishing between them (see Figure 27.30). (b) An eagles eye has a pupil with a diameter of 6.2 mm. Repeat part (a) for an eagle flying at the same altitude as the glider.

The French postimpressionist artist Georges Seurat developed a painting technique in which dots of color are placed close together on the canvas. From sufficiently far away the individual dots are not distinguishable, and the images in the picture take on a more normal appearance. Figure 27.31 shows a person in a museum looking at one of Seurats paintings. Suppose that the person stands close to the painting, then backs up until the dots just become indistinguishable to his eyes and takes a picture from this position. The light enters his eyes through pupils that have diameters of 2.5 mm and enters the digital camera through an aperture, or opening, with a diameter of 25 mm. He then goes home and prints an enlarged photograph of the painting. Can he see the individual dots in the photograph? (a) No, because if his eye cannot see the dots at the museum, the camera is also unable to record the individual dots. (b) Yes, because the camera gathers light through a much larger aperture than does the eye. (c) Yes, because, unlike the eye, a photograph taken by a camera is not limited by the effects of diffraction.

Suppose that the pupil of your eye were elliptical instead of circular in shape, with the long axis of the ellipse oriented in the vertical direction. Would the resolving power of your eye be the same in the horizontal and vertical directions and, if not, in which direction would it be greater? The resolving power would (a) be the same in both dire

Suppose that 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 (c) Small pupil and ultraviolet wavelengths

Review Conceptual Example 8 before answering this question. A person is viewing one of Seurats paintings that consists of dots of color. She is so close to the painting that the dots are distinguishable. Without moving, she squints, thus reducing the size of the opening in her eyes. Does squinting make the painting take on a more normal appearance?

On many 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 you want to resolve two closely spaced objects in a picture, should you use a small or a large f-number setting

A mixture of violet light ( 410 nm in vacuum) and red light ( 660 nm in vacuum) falls on a grating that contains 1.0  104 lines/cm. For each wavelength, find the angle that locates the first-order maxima. Reasoning Before Equation 2

The drawing shows a top view of a diffraction grating and the mth-order principal maxima that are obtained with red and blue light. Red light has the longer wavelength. (a) Which principal maximum is associated with blue light, the one farther from or the one closer to the central maximum? (b) If the number of slits per centimeter in the grating were increased, would these two principal maxima move away from the central maximum, move toward the central maximum, or remain in the same place?

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?

The laser in a CD player has a wavelength of 780 nm in a vacuum. The plastic coating over the pits has an index of refraction of n 1.5. Find the thickness of the pits on a CD.

A square is 3.5 m on a side, and point A is the midpoint of one of its sides. On the side opposite this spot, two in-phase loudspeakers are located at adjacent corners, as Figure 27.41 indicates. Standing at point A, you hear a loud sound because constructive interference occurs between the identical sound waves coming from the speakers. As you walk along the side of the square toward either empty corner, the loudness diminishes gradually but does not entirely disappear until you reach either empty corner, where you hear no sound at all. Thus, at each empty corner destructive interference occurs. Find the wavelength of the sound waves.

Why does constructive interference occur at point A?

What is the general condition that leads to destructive interference

The general condition that leads to destructive interference entails a number of possibilities. Which one of them, if any, applies at either empty corner of the squa

A soap film (n 1.33) is 375 nm thick and coats a flat piece of glass (n 1.52). Thus, air is on one side of the film and glass is on the other side, as Figure 27.42 illustrates. Sunlight, whose wavelengths (in vacuum) extend from 380 to 750 nm, travels through the air and strikes the film nearly perpendicularly. For which wavelength(s) in this range does constructive interference cause the film to look bright in reflected light? C

What, if any, phase change occurs when light, traveling in air, reflects from the airfilm interface?

What, if any, phase change occurs when light, traveling in the film, reflects from the filmglass interface?

Is the wavelength of the light in the film greater than, smaller than, or equal to the wavelength in a vacuum?

The two loudspeakers in the drawing are producing identical sound waves. The waves spread out and overlap at the point P. What is the difference 2 1 in the two path lengths if point P is at the third sound intensity minimum from the central sound intensity maximum? Express this difference in terms of the wavelength of the sound. (a) (b) (c) (d) 3 (e) Secti

In a certain Youngs double-slit experiment, a diffraction pattern is formed on a distant screen, as the drawing shows. The angle that locates a given bright fringe is small, so that the approximation sin  is valid. Assuming that remains small, by what factor does it change if the wavelength is doubled and the slit separation d is doubled? (a) The angle does not change. (b) The angle increases by a factor of 2. (c) The angle increases by a factor of 4. (d) The angle decreases by a factor of 2. (e) The angle decreases by a factor of 4. Bri

Light of wavelength 600 nm in vacuum is incident nearly perpendicularly on a thin film whose index of refraction is 1.5. The light travels from the top surface of the film to the bottom surface, reflects from the bottom surface, and returns to the top surface, as the drawing indicates. How far has the light traveled inside the film? Express your answer in terms of the wavelength film of the light within the film. (a) 2film (b) 3film (c) 4film (d) 6film (e) 12film 8. Li

Light is incident perpendicularly on four transparent films of different thickness. The thickness of each film is given in the drawings in terms of the wavelength film of the light within the film. The index of refraction of each film is 1.5, and each is surrounded by air. Which film (or films) will appear bright due to constructive interference when viewed from the top surface, upon which the light is incident? (a) 1, 2, 3, 4 (b) 2, 3 (c) 3 (d) 3, 4 (e) 4

Light passes through a single slit. If the width of the slit is reduced, what happens to the width of the central bright fringe? (a) The width of the central bright fringe does not change, because it depends only on the wavelength of the light and not on the width of the slit. (b) The central bright fringe becomes wider, because the angle that locates the first dark fringe on either side of the central bright fringe becomes smaller. (c) The central bright fringe becomes wider, because the angle that locates the first dark fringe on either side of the central bright fringe becomes larger. (d) The central bright fringe becomes narrower, because the angle that locates the first dark fringe on either side of the central bright fringe becomes larger. (e) The central bright fringe becomes narrower, because the angle that locates the first dark fringe on either side of the central bright fringe becomes smaller.

Light of wavelength passes through a single slit of width W and forms a diffraction pattern on a viewing screen. If this light is then replaced by light of wavelength 2, the original diffraction pattern is exactly reproduced if the width of the slit ______. (a) is changed to (b) is changed to (c) is changed to 2W (d) is changed to 4W (e) remains the sameno change is necessary 1

Suppose that you are using a microscope to view two closely spaced cells. For a given lens diameter, which color of light would you use to achieve the best possible resolving power? (a) Red (b) Yellow (c) Green (d) Blue (e) All the colors give the same resolving power.

A diffraction grating is illuminated with yellow light. The diffraction pattern seen on a viewing screen consists of three yellow bright fringes, one at the central maximum ( 0) and one on either side of it at 50. Then the grating is simultaneously illuminated with red light. Where a red and a yellow fringe overlap, an orange fringe is produced. The new pattern consists of _________. (a) only red fringes at 0 and 50 (b) only yellow fringes at 0 and 50 (c) only orange fringes at 0 and 50 (d) an orange fringe at 0, yellow fringes at 50, and red fringes farther out (e) an orange fringe at 0, yellow fringes at 50, and red fringes closer in c27

In a Youngs double-slit experiment, the wavelength of the light used is 520 nm (in vacuum), and the separation between the slits is 1.4  106 m. Determine the angle that locates (a) the dark fringe for which m 0, (b) the bright fringe for which m 1, (c) the dark fringe for which m 1, and (d) the bright fringe for which m 2. 2.

Two in-phase sources of waves are separated by a distance of 4.00 m. These sources produce identical waves that have a wavelength of 5.00 m. On the line between them, there are two places at which the same type of interference occurs. (a) Is it constructive or destructive interference, and (b) where are the places located?

The dark fringe for m 0 in a Youngs double-slit experiment is located at an angle of 15. What is the angle that locates the dark fringe for m 1? 5.

In a Youngs double-slit experiment, the seventh dark fringe is located 0.025 m to the side of the central bright fringe on a flat screen, which is 1.1 m away from the slits. The separation between the slits is 1.4  104 m. What is the wavelength of the light being used?

Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is A 645 nm. The other wavelength is B and is unknown. On a viewing screen, the light with wavelength A 645 nm produces its third-order bright fringe at the same place where where the light with wavelength B produces its fourth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?

In a setup like that in Figure 27.7, a wavelength of 625 nm is used in a Youngs double-slit experiment. The separation between the slits is d 1.4  105 m. The total width of the screen is 0.20 m. In one version of the setup, the separation between the double slit and the screen is LA 0.35 m, whereas in another version it is LB 0.50 m. On one side of the central bright fringe, how many bright fringes lie on the screen in the two versions of the setup? Do not include the central bright fringe in your counting. *

At most, how many bright fringes can be formed on either side of the central bright fringe when light of wavelength 625 nm falls on a double slit whose slit separation is 3.76  106 m?

In a Youngs double-slit experiment the separation y between the second-order bright fringe and the central bright fringe on a flat screen is 0.0180 m when the light has a wavelength of 425 nm. Assume that the angles that locate the fringes on the screen are small enough so that sin  tan . Find the separation y when the light has a wavelength of 585 nm.

In Youngs experiment a mixture of orange light (611 nm) and blue light (471 nm) shines on the double slit. The centers of the first-order bright blue fringes lie at the outer edges of a screen that is located 0.500 m away from the slits. However, the first-order bright orange fringes fall off the screen. By how much and in which direction (toward or away from the slits) should the screen be moved so that the centers of the first-order bright orange fringes will just appear on

A sheet that is made of plastic (n 1.60) covers one slit of a double slit (see the drawing). When the double slit is illuminated by monochromatic light (vacuum 586 nm), the center of the screen appears dark rather than bright. What is the minimum thickness of the plastic? S

You are standing in air and are looking at a flat piece of glass (n 1.52) on which there is a layer of transparent plastic (n 1.61). Light whose wavelength is 589 nm is vacuum is incident nearly perpendicularly on the coated glass and reflects into your eyes. The layer of plastic looks dark. Find the two smallest possible nonzero values for the thickness of the layer. 1

A nonreflective coating of magnesium fluoride (n 1.38) covers the glass (n 1.52) of a camera lens. Assuming that the coating prevents reflection of yellow-green light (wavelength in vacuum 565 nm), determine the minimum nonzero thickness that the coating can have.

When monochromatic light shines perpendicularly on a soap film (n 1.33) with air on each side, the second smallest nonzero film thickness for which destructive interference of reflected light is observed is 296 nm. What is the vacuum wavelength of the light in nm?

A transparent film (n 1.43) is deposited on a glass plate (n 1.52) to form a nonreflecting coating. The film has a thickness that is 1.07  107 m. What is the longest possible wavelength (in vacuum) of light for which this film has been designed? 1

A tank of gasoline (n 1.40) is open to the air (n 1.00). A thin film of liquid floats on the gasoline and has a refractive index that is between 1.00 and 1.40. Light that has a wavelength of 625 nm (in vacuum) shines perpendicularly down through the air onto this film, and in this light the film looks bright due to constructive interference. The thickness of the film is 242 nm and is the minimum nonzero thickness for which constructive interference can occur. What is the refractive index of the film? 1

Review Conceptual Example 4 before beginning this problem. A soap film with different thicknesses at different places has an unknown refractive index n and air on both sides. In reflected light it looks multicolored. One region looks yellow because destructive interference has removed blue (vacuum 469 nm) from the reflected light, while another looks magenta because destructive interference has removed green (vacuum 555 nm). In these regions the film has the minimum nonzero thickness t required for the destructive interference to occur. Find the ratio tmagenta/tyellow. * 1

A film of oil lies on wet pavement. The refractive index of the oil exceeds that of the water. The film has the minimum nonzero thickness such that it appears dark due to destructive interference when viewed in red light (wavelength 640.0 nm in vacuum). Assuming that the visible spectrum extends from 380 to 750 nm, for which visible wavelength(s) in vacuum will the film appear bright due to constructive interference?

Orange light (vacuum 611 nm) shines on a soap film (n 1.33) that has air on either side of it. The light strikes the film perpendicularly. What is the minimum thickness of the film for which constructive interference causes it to look bright in reflected light? Pr

The drawing shows a cross section of a planoconcave lens resting on a flat glass plate. (A planoconcave lens has one surface that is a plane and the other that is concave spherical.) The thickness t is 1.37  105 m. The lens is illuminated with monochromatic light (vacuum 550 nm), and a series of concentric bright and dark rings is formed, much like Newtons rings. How many bright rings are there? (Hint: The cross section shown in the drawing reveals that a kind of air wedge exists between the place where the two pieces of glass touch and the top of the curved surface where the distance t is marked.) **

A piece of curved glass has a radius of curvature of r 10.0 m and is used to form Newtons rings, as in Figure 27.13. Not counting the dark spot at the center of the pattern, there are one hundred dark fringes, the last one being at the outer edge of the curved piece of glass. The light being used has a wavelength of 654 nm in vacuum. What is the radius R of the outermost dark ring in the pattern? (Hint: Note that r is much greater than R, and you may assume that tan for small angles, where must be expressed in radians.) *

A uniform layer of water (n 1.33) lies on a glass plate (n 1.52). Light shines perpendicularly on the layer. Because of constructive interference, the layer looks maximally bright when the wavelength of the light is 432 nm in vacuum and also when it is 648 nm in vacuum. (a) Obtain the minimum thickness of the film. (b) Assuming that the film has the minimum thickness and that the visible spectrum extends from 380 to 750 nm, determine the visible wavelength(s) in vacuum for which the film appears completely dark. S

(a) As Section 17.3 discusses, high-frequency sound waves exhibit less diffraction than low-frequency sound waves do. However, even highfrequency sound waves exhibit much more diffraction under normal circumstances than do light waves that pass through the same opening. The highest frequency that a healthy ear can typically hear is 2.0  104 Hz. Assume that a sound wave with this frequency travels at 343 m/s and passes through a doorway that has a width of 0.91 m. Determine the angle that locates the first minimum to either side of the central maximum in the diffraction pattern for the sound. This minimum is equivalent to the first dark fringe in a single-slit diffraction pattern for light. (b) Suppose that yellow light (wavelength 580 nm in vacuum) passes through a doorway and that the first dark fringe in its diffraction pattern is located at the angle determined in part (a). How wide would this hypothetical doorway have to be?

A dark fringe in the diffraction pattern of a single slit is located at an angle of A 34. With the same light, the same dark fringe formed with another single slit is at an angle of B 56. Find the ratio WA/WB of the widths of the two slits. 25. s

A diffraction pattern forms when light passes through a single slit. The wavelength of the light is 675 nm. Determine the angle that locates the first dark fringe when the width of the slit is (a) 1.8  104 m and (b) 1.8  106 m.

A slit has a width of W1 2.3  106 m. When light with a wavelength of 1 510 nm passes through this slit, the width of the central bright fringe on a flat observation screen has a certain value. With the screen kept in the same place, this slit is replaced with a second slit (width W2), and a wavelength of 2 740 nm is used. The width of the central bright fringe on the screen is observed to be unchanged. Find W2. 27.

Light that has a wavelength of 668 nm passes through a slit 6.73  106 m wide and falls on a screen that is 1.85 m away. What is the distance on the screen from the center of the central bright fringe to the third dark fringe on either side?

Light shines through a single slit whose width is 5.6  104 m. A diffraction pattern is formed on a flat screen located 4.0 m away. The distance between the middle of the central bright fringe and the first dark fringe is 3.5 mm. What is the wavelength of the light?

Light waves with two different wavelengths, 632 nm and 474 nm, pass simultaneously through a single slit whose width is 7.15  105 m and strike a screen 1.20 m from the slit. Two diffraction patterns are formed on the screen. What is the distance (in cm) between the common center of the diffraction patterns and the first occurrence of a dark fringe from one pattern falling on top of a dark fringe from the other pattern?

The central bright fringe in a single-slit diffraction pattern has a width that equals the distance between the screen and the slit. Find the ratio /W of the wavelength of the light to the width W of the slit. * 31. ssm How many dark fringes will be produced on either side of the central maximum if light ( 651 nm) is incident on a single slit that is 5.47  106 m wide? ** 3

In a single-slit diffraction pattern, the central fringe is 450 times as wide as the slit. The screen is 18 000 times farther from the slit than the slit is wide. What is the ratio /W, where is the wavelength of the light shining through the slit and W is the width of the slit? Assume that the angle that locates a dark fringe on the screen is small, so that sin  tan . Sec

Two stars are 3.7  1011 m apart and are equally distant from the earth. A telescope has an objective lens with a diameter of 1.02 m and just detects these stars as separate objects. Assume that light of wavelength 550 nm is being observed. Also assume that diffraction effects, rather than atmospheric turbulence, limit the resolving power of the telescope. Find the maximum distance that these stars could be from the earth.

It is claimed that some professional baseball players can see which way the ball is spinning as it travels toward home plate. One way to judge this claim is to estimate the distance at which a batter can first hope to resolve two points on opposite sides of a baseball, which has a diameter of 0.0738 m. (a) Estimate this distance, assuming that the pupil of the eye has a diameter of 2.0 mm and the wavelength of the light is 550 nm in vacuum. (b) Considering that the distance between the pitchers mound and home plate is 18.4 m, can you rule out the claim based on your answer to part (a)?

Late one night on a highway, a car speeds by you and fades into the distance. Under these conditions the pupils of your eyes have diameters of about 7.0 mm. The taillights of this car are separated by a distance of 1.2 m and emit red light (wavelength 660 nm in vacuum). How far away from you is this car when its taillights appear to merge into a single spot of light because of the effects of diffraction?

An inkjet printer uses tiny dots of red, green, and blue ink to produce an image. Assume that the dot separation on the printed page is the same for all colors. At normal viewing distances, the eye does not resolve the individual dots, regardless of color, so that the image has a normal look. The wavelengths for red, green, and blue are red 660 nm, green 550 nm, and blue 470 nm. The diameter of the pupil through which light enters the eye is 2.0 mm. For a viewing distance of 0.40 m, what is the maximum allowable dot separation? 37. A

A hunter who is a bit of a braggart claims that from a distance of 1.6 km he can selectively shoot either of two squirrels who are sitting ten centimeters apart on the same branch of a tree. Whats more, he claims that he can do this without the aid of a telescopic sight on his rifle. (a) Determine the diameter of the pupils of his eyes that would be required for him to be able to resolve the squirrels as separate objects. In this calculation use a wavelength of 498 nm (in vacuum) for the light. (b) State whether his claim is reasonable, and provide a reason for your answer. In evaluating his claim, consider that the human eye automatically adjusts the diameter of its pupil over a typical range of 2 to 8 mm, the larger values coming into play as the lighting becomes darker. Note also that under dark conditions, the eye is most sensitive to a wavelength of 498 nm.

Review Conceptual Example 8 as background for this problem. In addition to the data given there, assume that the dots in the painting are separated by 1.5 mm and that the wavelength of the light is vacuum 550 nm. Find the distance at which the dots can just be resolved by (a) the eye and (b) the camera.

Astronomers have discovered a planetary system orbiting the star Upsilon Andromedae, which is at a distance of 4.2  1017 m from the earth. One planet is believed to be located at a distance of 1.2  1011 m from the star. Using visible light with a vacuum wavelength of 550 nm, what is the minimum necessary aperture diameter that a telescope must have so that it can resolve the planet and the star?

The pupil of an eagles eye has a diameter of 6.0 mm. Two field mice are separated by 0.010 m. From a distance of 176 m, the eagle sees them as one unresolved object and dives toward them at a speed of 17 m/s. Assume that the eagles eye detects light that has a wavelength of 550 nm in vacuum. How much time passes until the eagle sees the mice as separate objects?

Consult Multiple-Concept Example 7 to see a model for solving this kind of problem. You are using a microscope to examine a blood sample. Recall from Section 26.12 that the sample should be placed just outside the focal point of the objective lens of the microscope. (a) If the specimen is being illuminated with light of wavelength and the diameter of the objective equals its focal length, determine the closest distance between two blood cells that can just be resolved. Express your answer in terms of . (b) Based on your answer to (a), should you use light with a longer wavelength or a shorter wavelength if you wish to resolve two blood cells that are even closer together? *

Two concentric circles of light emit light whose wavelength is 555 nm. The larger circle has a radius of 4.0 cm, and the smaller circle has a radius of 1.0 cm. When taking a picture of these lighted circles, a camera admits light through an aperture whose diameter is 12.5 mm. What is the maximum distance at which the camera can (a) distinguish one circle from the other and (b) reveal that the inner circle is a circle of light rather than a solid disk of light?

A diffraction grating is 1.50 cm wide and contains 2400 lines. When used with light of a certain wavelength, a third-order maximum is formed at an angle of 18.0. What is the wavelength (in nm)?

The light shining on a diffraction grating has a wavelength of 495 nm (in vacuum). The grating produces a second-order bright fringe whose position is defined by an angle of 9.34. How many lines per centimeter does the grating have?

For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 26. For an unknown wavelength, the same grating produces a bright fringe at an angle of 41. In both cases the bright fringes are of the same order m. What is the unknown wavelength? 4

Two diffraction gratings, A and B, are located at the same distance from the observation screens. Light with the same wavelength is used for each. The separation between adjacent principal maxima for grating A is 2.7 cm, and for grating B it is 3.2 cm. Grating A has 2000 lines per meter. How many lines per meter does grating B have? (Hint: The diffraction angles are small enough that the approximation sin tan can be used.) 47.

The wavelength of the laser beam used in a compact disc player is 780 nm. Suppose that a diffraction grating produces first-order tracking beams that are 1.2 mm apart at a distance of 3.0 mm from the grating. Estimate the spacing between the slits of the grating.

The first-order principle maximum produced by a grating is located at an angle of 18.0. What is the angle for the third-order maximum with the same light? *

A diffraction grating has 2604 lines per centimeter, and it produces a principal maximum at 30.0. The grating is used with light that contains all wavelengths between 410 and 660 nm. What is (are) the wavelength(s) of the incident light that could have produced this maximum? *

Violet light (wavelength 410 nm) and red light (wavelength 660 nm) lie at opposite ends of the visible spectrum. (a) For each wavelength, find the angle that locates the first-order maximum produced by a grating with 3300 lines/cm. This grating converts a mixture of all colors between violet and red into a rainbow-like dispersion between the two angles. Repeat the calculation above for (b) the secondorder maximum and (c) the third-order maximum. (d) From your results, decide whether there is an overlap between any of the rainbows and, if so, specify which orders overlap. *

The distance between adjacent slits of a certain diffraction grating is 1.250  105 m. The grating is illuminated by monochromatic light with a wavelength of 656.0 nm, and is then heated so that its temperature increases by 100.0 C. Determine the change in the angle of the seventhorder principal maximum that occurs as a result of the thermal expansion of the grating. The coefficient of linear expansion for the diffraction grating is 1.30  104 (C) 1 . Be sure to include the proper algebraic sign with your answer:  if the angle increases,  if the angle decreases. *

Two gratings A and B have slit separations d A and dB, respectively. They are used with the same light and the same observation screen. When grating A is replaced with grating B, it is observed that the firstorder maximum of A is exactly replaced by the second-order maximum of B. (a) Determine the ratio dB/dA of the spacings between the slits of the gratings. (b) Find the next two principal maxima of grating A and the principal maxima of B that exactly replace them when the gratings are switched. Identify these maxima by their order numbers.

A soap film (n 1.33) is 465 nm thick and lies on a glass plate (n 1.52). Sunlight, whose wavelengths (in vacuum) extend from 380 to 750 nm, travels through the air and strikes the film perpendicularly. For which wavelength(s) in this range does destructive interference cause the film to look dark in reflected light?

In a Youngs double-slit experiment, two rays of monochromatic light emerge from the slits and meet at a point on a distant screen, as in Figure 27.6a. The point on the screen where these two rays meet is the eighth-order bright fringe. The difference in the distances that the two rays travel is 4.57  106 m. What is the wavelength (in nm) of the monochromatic light?

Point A is the midpoint of one of the sides of a square. On the side opposite this spot, two in-phase loudspeakers are located at adjacent corners, as in Figure 27.41. Standing at point A you hear a loud sound because of constructive interference between the identical sound waves coming from the speakers. As you walk along the side of the square toward either empty corner, the loudness diminishes gradually to nothing and then increases again until you hear a maximally loud sound at the corner. If the length of each side of the square is 4.6 m, find the wavelength of the sound waves.

A flat observation screen is placed at a distance of 4.5 m from a pair of slits. The separation on the screen between the central bright fringe and the first-order bright fringe is 0.037 m. The light illuminating the slits has a wavelength of 490 nm. Determine the slit separation.

A flat screen is located 0.60 m away from a single slit. Light with a wavelength of 510 nm (in vacuum) shines through the slit and produces a diffraction pattern. The width of the central bright fringe on the screen is 0.050 m. What is the width of the slit?

A large group of football fans comes to the game with colored cards that spell out the name of their team when held up simultaneously. Most of the cards are colored blue (vacuum 480 nm). When displayed, the average distance between neighboring cards is 5.0 cm. If the cards are to blur together into solid blocks of color when viewed by a spectator at the other end of the stadium (160 m away), what must be the maximum diameter (in mm) of the spectators pupils?

Review Conceptual Example 2 before attempting this problem. Two slits are 0.158 mm apart. A mixture of red light (wavelength 665 nm) and yellow-green light (wavelength 565 nm) falls on the slits. A flat observation screen is located 2.24 m away. What is the distance on the screen between the third-order red fringe and the third-order yellowgreen fringe? *

The same diffraction grating is used with two different wavelengths of light, A and B. The fourth-order principal maximum of light A exactly overlaps the third-order principal maximum of light B. Find the ratio A/B. * 6

A spotlight sends red light (wavelength 694.3 nm) to the moon. At the surface of the moon, which is 3.77  108 m away, the light strikes a reflector left there by astronauts. The reflected light returns to the earth, where it is detected. When it leaves the spotlight, the circular beam of light has a diameter of about 0.20 m, and diffraction causes the beam to spread as the light travels to the moon. In effect, the first circular dark fringe in the diffraction pattern defines the size of the central bright spot on the moon. Determine the diameter (not the radius) of the central bright spot on the moon.

In a single-slit diffraction pattern on a flat screen, the central bright fringe is 1.2 cm wide when the slit width is 3.2  105 m. When the slit is replaced by a second slit, the wavelength of the light and the distance to the screen remaining unchanged, the central bright fringe broadens to a width of 1.9 cm. What is the width of the second slit? It may be assumed that is so small that sin  tan .

A beam of light is sent directly down onto a glass plate (n 1.5) and a plastic plate (n 1.2) that form a thin wedge of air (see the drawing). An observer looking down through the glass plate sees the fringe pattern shown in the lower part of the drawing, with the dark fringes at the ends A and B. The wavelength of the light is 520 nm. Using the fringe pattern shown in the drawing, determine the thickness of the air wedge at B. *

There are 5620 lines per centimeter in a grating that is used with light whose wavelength is 471 nm. A flat observation screen is located at a distance of 0.750 m from the grating. What is the minimum width that the screen must have so the centers of all the principal maxima formed on either side of the central maximum fall on the screen?

A circular drop of oil lies on a smooth, horizontal surface. The drop is thickest in the center and tapers to zero thickness at the edge. When illuminated from above by blue light ( 455 nm), 56 concentric bright rings are visible, including a bright fringe at the edge of the drop. In addition, there is a bright spot in the center of the drop. When the drop is illuminated from above by red light ( 637 nm), a bright spot again appears at the center, along with a different number of bright rings. Ignoring the bright spot, how many bright rings appear in red light? Assume that the index of refraction of the oil is the same for both wavelengths. Pla

Light of wavelength 410 nm (in vacuum) is incident on a diffraction grating that has a slit separation of 1.2  105 m. The distance between the grating and the viewing screen is 0.15 m. A diffraction pattern is produced on the screen that consists of a central bright fringe and higher-order bright fringes (see the drawing). (a) Determine the distance y from the central bright fringe to the second-order bright fringe. (Hint: The diffraction angles are small enough that the approximation tan sin can be used.) (b) If the entire apparatus is submerged in water (nwater 1.33), what is the distance y? Add