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physics
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Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

Two lenses, separated by a distance of 21.0 cm, are used in combination. The first lens has a focal length of + 30.0 cm; the second has a focal length of − 15.0 cm. An object, 2.0 mm long, is placed 1.8 cm before the first lens. (a) What are the intermediate and final image distances relative to
A camera lens has a fixed focal length of magnitude 50.0 mm. The camera is focused on a 1.0-m-tall child who is standing 3.0 m from the lens. (a) Should the image formed be real or virtual? Why? (b) Is the lens converging or diverging? Why? (c) What is the distance from the lens to the film? (d)
A camera with a 50.0-mm lens can focus on objects located from 1.5 m to an infinite distance away by adjusting the distance between the lens and the film. When the focus is changed from that for a distant mountain range to that for a flower bed at 1.5 m, how far does the lens move with respect to
The area occupied by one frame on 35-mm film is 24 mm by 36 mm-see the figure with Problem 16. The focal length of the camera lens is 50.0 mm. A picture is taken of a person 182 cm tall. What is the minimum distance from the camera for the person to stand so that the image fits on the film? Give
A dissecting microscope is designed to have a large distance between the object and the objective lens. Suppose the focal length of the objective of a dissecting microscope is 5.0 cm, the focal length of the eyepiece is 4.0 cm, and the distance between the lenses is 32.0 cm. (a) What is the
A cub scout makes a simple microscope by placing two converging lenses of + 18 D at opposite ends of a 28-cmlong tube. (a) What is the tube length of the microscope? (b) What is the angular magnification? (c) How far should an object be placed from the objective lens?
Verify the locations and sizes of the images formed by the two lenses in Fig. 24.1b using the lens equation and the following data: f1 = + 4.00 cm, f2 = − 2.00 cm, s = 8.00 cm (where s is the distance between the lenses), p1 = + 6.00 cm, and h = 2.00 mm.
A convex lens of power + 12 D is used as a magnifier to examine a wildflower. What is the angular magnification if the final image is at? (a) Infinity (b) The near point of 25 cm
A refracting telescope has an objective lens with a focal length of 2.20 m and an eyepiece with a focal length of 1.5 cm. If you look through this telescope the wrong way that is, with your eye placed at the objective lens, by what factor is the angular size of an observed object reduced?
Suppose the distance from the lens system of the eye (cornea + lens) to the retina is 18 mm. (a) What must the power of the lens be when looking at distant objects? (b) What must the power of the lens be when looking at an object 20.0 cm from the eye? (c) Suppose that the eye is farsighted; the
An object is placed 7.00 cm to the left of a converging lens of focal length 3.00 cm. A convex mirror with a radius of curvature of 4.00 cm is placed 12.00 cm to the right of the lens.(a) Where is the intermediate image formed by the lens?(b) Is the intermediate image real or virtual and is it
Veronique is nearsighted; she cannot see clearly anything more than 6.00 m away without her contacts. One day she doesn't wear her contacts; rather, she wears an old pair of glasses prescribed when she could see clearly up to 8.00 m away. Assume the glasses are 2.0 cm from her eyes. What is the
A man requires reading glasses with +2.0 D power to read a book held 40.0 cm away with a relaxed eye. Assume the glasses are 2.0 cm from his eyes. (a) What is his uncorrected far point? (b) What refractive power lenses should he use for distance vision? (c) His uncorrected near point is 1.0 m. What
A microscope has an eyepiece of focal length 2.00 cm and an objective of focal length 3.00 cm. The eyepiece produces a virtual image at the viewer's near point (25.0 cm from the eye). (a) How far from the eyepiece is the image formed by the objective? (b) If the lenses are 20.0 cm apart, what is
Show that if two thin lenses are close together (s, the distance between the lenses, is negligibly small), the two lenses can be replaced by a single equivalent lens with focal length feq. Find the value of feq in terms of f1 and f2.
You would like to project an upright image at a position 32.0 cm to the right of an object. You have a converging lens with focal length 3.70 cm located 6.00 cm to the right of the object. By placing a second lens at 24.65 cm to the right of the object, you obtain an image in the proper
Explain why two waves of significantly different frequencies cannot be coherent.
What are some of the advantages of a UV microscope over a visible light microscope? What are some of the disadvantages?
In Section 25.3 we studied interference due to thin films. Why must the film be thin? Why don't we see interference effects when looking through a window or at a poster covered by a plate of glass-even if the glass is optically flat?
Explain, using Huygens's principle, why the Poisson spot is expected.
What effect places a lower limit on the size of an object that can be clearly seen with the best optical microscope?
A lens (n = 1.51) has an antireflective coating of MgF2 (n = 1.38). Which of the first two reflected rays has a phase shift of 180°? Suppose a different antireflective coating on a similar lens had n = 1.62. Now which of the first two reflected rays has a phase shift of 180°?
In the microwave experiment of Example 25.1 and in the Michelson interferometer, we ignored phase changes due to reflection from a metal surface. Microwaves and light are inverted when they reflect from metal. Why were we able to ignore the 180 ° phase shifts?
Why does a crystal act as a three-dimensional grating for x-rays but not for visible light?
Why do eyeglasses, cameras lenses, and binoculars with antireflective coatings often look faintly purple?
Telescopes used in astronomy have large lenses (or mirrors). One reason is to let a lot of light in important for seeing faint astronomical bodies. Can you think of another reason why it is an advantage to make these telescopes so large?
The Hubble Space Telescope uses a mirror of radius 1.2 m. Is its resolution better when detecting visible light or UV? Explain.
Why can you easily hear sound around a corner due to diffraction, while you cannot see around the same corner?
Stereo speakers should be wired with the same polarity. If by mistake they are wired with opposite polarities, the bass (low frequencies) sound much weaker than if they are wired correctly. Why? Why is the bass (low frequencies) weakened more than the treble (high frequencies)?
Two antennas driven by the same electrical signal emit coherent radio waves. Is it possible for two antennas driven by independent signals to emit radio waves that are coherent with each other? If so, how? If not, why not?
A radio station wants to ensure good reception of its signal everywhere inside a city. Would it be a good idea to place several broadcasting antennas at roughly equal intervals around the perimeter of the city? Explain.
The size of an atom is about 0.1 nm. Can a light microscope make an image of an atom? Explain.
A 60-kHz radio transmitter sends an electromagnetic wave to a receiver 21 km away. The signal also travels to the receiver by another path where it reflects from a helicopter as shown. Assume that there is a 180 ° phase shift when the wave is reflected.(a) What is the wavelength of this EM
The feathers of the ruby-throated hummingbird have an iridescent green color due to interference. A simplified model of the step structure of the feather is shown in the figure. If the strongest reflection for normal incidence is at Î» = 520 nm, what is the step height h? Assume h has
A Michelson interferometer is adjusted so that a bright fringe appears on the screen. As one of the mirrors is moved 25.8 μ m, 92 bright fringes are counted on the screen. What is the wavelength of the light used in the interferometer?
Suppose a transparent vessel 30.0 cm long is placed in one arm of a Michelson interferometer, as in Example 25.2. The vessel initially contains air at 0 ° C and 1.00 atm. With light of vacuum wavelength 633 nm, the mirrors are arranged so that a bright spot appears at the center of the screen. As
A Michelson interferometer is set up using white light. The arms are adjusted so that a bright white spot appears on the screen (constructive interference for all wavelengths). A slab of glass (n = 1.46) is inserted into one of the arms. To return to the white spot, the mirror in the other arm is
At a science museum, Marlow looks down into a display case and sees two pieces of very flat glass lying on top of each other with light and dark regions on the glass. The exhibit states that monochromatic light with a wavelength of 550 nm is incident on the glass plates and that the plates are
See Problem 14. This time the glass plates are immersed in clear oil with an index of refraction of 1.50. (a) What is the minimum distance between the two glass plates for one of the dark regions? (b) What is the minimum distance between the two glass plates for one of the light regions? (c)
A thin film of oil (n = 1.50) is spread over a puddle of water (n = 1.33). In a region where the film looks red from directly above (l = 630 nm), what is the minimum possible thickness of the film?
A thin film of oil (n = 1.50) of thickness 0.40 μ m is spread over a puddle of water (n = 1.33). For which wavelength in the visible spectrum do you expect constructive interference for reflection at normal incidence?
A transparent film (n = 1.3) is deposited on a glass lens (n = 1.5) to form a non reflective coating. What is the minimum thickness that would minimize reflection of light with wavelength 500.0 nm in air?
A camera lens (n = 1.50) is coated with a thin film of magnesium fluoride (n = 1.38) of thickness 90.0 nm. What wavelength in the visible spectrum is most strongly transmitted through the film?
A steep cliff west of Lydia's home reflects a 1020-kHz radio signal from a station that is 74 km due east of her home. If there is destructive interference, what is the minimum distance of the cliff from her home? Assume there is a 180 ° phase shift when the wave reflects from the cliff.
A soap film has an index of refraction n = 1.50. The film is viewed in reflected light. (a) At a spot where the film thickness is 910.0 nm, which wavelengths are missing in the reflected light? (b) Which wavelengths are strongest in reflected light?
A soap film has an index of refraction n = 1.50. The film is viewed in transmitted light. (a) At a spot where the film thickness is 910.0 nm, which wavelengths are weakest in the transmitted light? (b) Which wavelengths are strongest in transmitted light?
Two optically flat plates of glass are separated at one end by a wire of diameter 0.200 mm; at the other end they touch. Thus, the air gap between the plates has a thickness ranging from 0 to 0.200 mm. The plates are 15.0 cm long and are illuminated from above with light of wavelength 600.0 nm. How
A lens is placed on a flat plate of glass to test whether its surface is spherical.(a) Show that the radius rm of the m th dark ring should beWhere R is the radius of curvature of the lens surface facing the plate and the wavelength of the light used is l. Assume that rm (b) Are the dark fringes
A thin film is viewed both in reflected and transmitted light at normal incidence. The figure shows the strongest two rays for each. Show that if rays 1 and 2 interfere constructively, then rays 3 and 4 must interfere destructively, and if rays 1 and 2 interfere destructively, then rays 3 and 4
Repeat Problem 24 assuming that n1 < n2 < n3.
Light of 650 nm is incident on two slits. A maximum is seen at an angle of 4.10° and a minimum of 4.78°. What is the order m of the maximum and what is the distance d between the slits?
You are given a slide with two slits cut into it and asked how far apart the slits are. You shine white light on the slide and notice the first-order color spectrum that is created on a screen 3.40 m away. On the screen, the red light with a wavelength of 700 nm is separated from the violet light
Show that the interference fringes in a double-slit experiment are equally spaced on a distant screen near the center of the interference pattern.
Use a compass to make an accurate drawing of the wave fronts in a double-slit interference experiment similar to Fig. 25.18c. Place the slits 2.0 cm apart and let the wavelength of the incident wave be 1.0 cm. Using a straightedge, draw lines of constructive interference (antinodes) and use them to
Roger is in a ship offshore and listening to a baseball game on his radio. He notices that there is destructive interference when seaplanes from the nearby Coast Guard station are flying directly overhead at elevations of 780 m, 975 m, and 1170 m. The broadcast station is 102 km away. Assume there
In a double-slit interference experiment, the wavelength is 475 nm, the slit separation is 0.120 mm, and the screen is 36.8 cm away from the slits. What is the linear distance between adjacent maxima on the screen?
Light incident on a pair of slits produces an interference pattern on a screen 2.50 m from the slits. If the slit separation is 0.0150 cm and the distance between adjacent bright fringes in the pattern is 0.760 cm, what is the wavelength of the light?
Ramon has a coherent light source with wavelength 547 nm. He wishes to send light through a double slit with slit separation of 1.50 mm to a screen 90.0 cm away. What is the minimum width of the screen if Ramon wants to display five interference maxima?
Light from a helium-neon laser (630 nm) is incident on a pair of slits. In the interference pattern on a screen 1.5 m from the slits, the bright fringes are separated by 1.35 cm. What is the slit separation?
Light of wavelength 589 nm incident on a pair of slits produces an interference pattern on a distant screen in which the separation between adjacent bright fringes at the center of the pattern is 0.530 cm. A second light source, when incident on the same pair of slits, produces an interference
A double slit is illuminated with monochromatic light of wavelength 600.0 nm. The m = 0 and m = 1 bright fringes are separated by 3.0 mm on a screen 40.0 cm away from the slits. What is the separation between the slits?
A grating has exactly 8000 slits uniformly spaced over 2.54 cm and is illuminated by light from a mercury vapor discharge lamp. What is the expected angle for the third-order maximum of the green line (λ = 546 nm)?
A red line (wavelength 630 nm) in the third order overlaps with a blue line in the fourth order for a particular grating. What is the wavelength of the blue line?
Red light of 650 nm can be seen in three orders in a particular grating. About how many slits per centimeter does this grating have?
A grating has 5000.0 slits / cm. How many orders of violet light of wavelength 412 nm can be observed with this grating?
Sketch a sinusoidal wave with amplitude of 2 cm and a wavelength of 6 cm. This wave represents the electric field portion of a visible EM wave traveling to the right with intensity I0. (a) Sketch an identical wave beneath the first. What is the amplitude (in centimeters) of the sum of these waves?
A grating is made of exactly 8000 slits; the slit spacing is 1.50 μ m. Light of wavelength 0.600 μ m is incident normally on the grating. (a) How many maxima are seen in the pattern on the screen? (b) Sketch the pattern that would appear on a screen 3.0 m from the grating. Label distances from
A reflection grating spectrometer is used to view the spectrum of light from a helium discharge tube. The three brightest spectral lines seen are red, yellow, and blue in color. These lines appear at the positions labeled A, B, and C in the figure, though not necessarily in that order of color. In
White light containing wavelengths from 400 nm to 700 nm is shone through a grating. Assuming that at least part of the third-order spectrum is present, show that the second and third-order spectra always overlap, regardless of the slit separation of the grating
A grating 1.600 cm wide has exactly 12 000 slits. The grating is used to resolve two nearly equal wavelengths in a light source: λa = 440.000 nm and λb = 440.936 nm. (a) How many orders of the lines can be seen with the grating? (b) What is the angular separation θb - θa between the lines in
A grating spectrometer is used to resolve wavelengths 660.0 nm and 661.4 nm in second order. (a) How many slits per centimeter must the grating have to produce both wavelengths in second order? (The answer is either a maximum or a minimum number of slits per centimeter.) (b) The minimum number of
The central bright fringe in a single-slit diffraction pattern from light of wavelength 476 nm is 2.0 cm wide on a screen that is 1.05 m from the slit. (a) How wide is the slit? (b) How wide are the first two bright fringes on either side of the central bright fringe? (Define the width of a bright
The first two dark fringes on one side of the central maximum in a single-slit diffraction pattern are 1.0 mm apart. The wavelength of the light is 610 nm and the screen is 1.0 m from the slit. What is the slit width?
Light of wavelength 630 nm is incident on a single slit with width 0.40 mm. The figure shows the pattern observed on a screen positioned 2.0 m from the slit. Determine the distance from the center of the central bright fringe to the second minimum on one side.
Light from a red laser passes through a single slit to form a diffraction pattern on a distant screen. If the width of the slit is increased by a factor of two, what happens to the width of the central maximum on the screen?
The diffraction pattern from a single slit is viewed on a screen. Using blue light, the width of the central maximum is 2.0 cm. (a) Would the central maximum be narrower or wider if red light is used instead? (b) If the blue light has wavelength 0.43 μ m and the red light has wavelength 0.70 μ
Light of wavelength 490 nm is incident on a narrow slit. The diffraction pattern is viewed on a screen 3.20 m from the slit. The distance on the screen between the central maximum and the third minimum is 2.5 cm. What is the width of the slit?
The Hubble Space Telescope (HST) has excellent resolving power because there is no atmospheric distortion of the light. Its 2.4-m-diameter primary mirror can collect light from distant galaxies that formed early in the history of the universe. How far apart can two galaxies be from each other if
A beam of yellow laser light (590 nm) passes through a circular aperture of diameter 7.0 mm what is the angular width of the central diffraction maximum formed on a screen?
The photosensitive cells (rods and cones) in the retina are most densely packed in the fovea-the part of the retina used to see straight ahead. In the fovea, the cells are all cones spaced about 1 μ m apart. Would our vision have much better resolution if they were closer together? To answer this
The radio telescope at Arecibo, Puerto Rico, has a reflecting spherical bowl of 305 m (1000 ft) diameter. Radio signals can be received and emitted at various frequencies with appropriate antennae at the focal point of the reflecting bowl. At a frequency of 300 MHz, what is the angle between two
A pinhole camera doesn't have a lens; a small circular hole lets light into the camera, which then exposes the film. For the sharpest image, light from a distant point source makes as small a spot on the film as possible. What is the optimum size of the hole for a camera in which the film is 16.0
To understand Rayleigh's criterion as applied to the pupil of the eye, notice that rays do not pass straight through the center of the lens system (cornea + lens) of the eye except at normal incidence because the indices of refraction on the two sides of the lens system are different. In a
A beam of coherent light of wavelength 623 nm in air is incident on a rectangular block of glass with index of refraction 1.40. If, after emerging from the block, the wave that travels through the glass is 180 ° out of phase with the wave that travels through air, what are the possible lengths
Light with a wavelength of 660 nm is incident on two slits and the pattern shown in the figure is viewed on a screen. Point A is directly opposite a point midway between the two slits. What is the path length difference of the light that passes through the two different slits for light that reaches
A thin layer of an oil (n = 1.60) floats on top of water (n = 1.33). One portion of this film appears green (λ = 510 nm) in reflected light. How thick is this portion of the film? Give the three smallest possibilities.
If diffraction were the only limitation, what would be the maximum distance at which the headlights of a car could be resolved (seen as two separate sources) by the naked human eye? The diameter of the pupil of the eye is about 7 mm when dark-adapted. Make reasonable estimates for the distance
Find the height h of the pits on a CD (Fig. 25.6a). When the laser beam reflects partly from a pit and partly from land (the flat aluminum surface) on either side of the "pit," the two reflected beams interfere destructively; h is chosen to be the smallest possible height that causes destructive
The Very Large Array (VLA) is a set of 30 dish radio antennas located near Socorro, New Mexico. The dishes are spaced 1.0 km apart and form a Y-shaped pattern, as in the diagram. Radio pulses from a distant pulsar (a rapidly rotating neutron star) are detected by the dishes; the arrival time of
Two narrow slits with a center-to-center distance of 0.48 mm are illuminated with coherent light at normal incidence. The intensity of the light falling on a screen 5.0 m away is shown in the figure, where x is the distance from the central maximum on the screen.(a) What would be the intensity of
When a double slit is illuminated with light of wavelength 510 nm, the interference maxima on a screen 2.4 m away gradually decrease in intensity on either side of the 2.40-cm-wide central maximum and reach a minimum in a spot where the fifth-order maximum is expected. (a) What is the width of the
Sonya is designing a diffraction experiment for her students. She has a laser that emits light of wavelength 627 nm and a grating with a distance of 2.40 × 10−3 mm between slits. She hopes to shine the light through the grating and display a total of nine interference maxima on a screen. She
A lens (n = 1.52) is coated with a magnesium fluoride film (n = 1.38). (a) If the coating is to cause destructive interference in reflected light for λ = 560 nm (the peak of the solar spectrum), what should its minimum thickness be? (b) At what two wavelengths closest to 560 nm does the coating
Instead of an antireflective coating, suppose you wanted to coat a glass surface to enhance the reflection of visible light. Assuming that 1 < ncoating < nglass, what should the minimum thickness of the coating be to maximize the reflected intensity for wavelength λ?
In bright light, the pupils of the eyes of a cat narrow to a vertical slit 0.30 mm across. Suppose that a cat is looking at two mice 18 m away. What is the smallest distance between the mice for which the cat can tell that there are two mice rather than one using light of 560 nm? Assume the
Parallel light of wavelength l strikes a slit of width a at normal incidence. The light is viewed on a screen that is 1.0 m past the slits. In each case that follows, sketch the intensity on the screen as a function of x, the distance from the center of the screen, for 0 ≤ x ≤ 10 cm. (a) l = 10
About how close to each other are two objects on the Moon that can just barely be resolved by the 5.08-m- (200-in.) - diameter Mount Palomar reflecting telescope? (Use a wavelength of 520 nm.)
A grating in a spectrometer is illuminated with red light (λ = 690 nm) and blue light (λ = 460 nm) simultaneously. The grating has 10,000.0 slits/cm. Sketch the pattern that would be seen on a screen 2.0 m from the grating. Label distances from the central maximum. Label which lines are red and
Two slits separated by 20.0 μ m are illuminated by light of wavelength 0.50 μ m. If the screen is 8.0 m from the slits, what is the distance between the m = 0 and m = 1 bright fringes?
In a double-slit experiment, what is the linear distance on the screen between adjacent maxima if the wavelength is 546 nm, the slit separation is 0.100 mm, and the slit-screen separation is 20.0 cm?

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