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college physics reasoning
College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions
You have two unlabeled laser discs, one a CD and the other a DVD. Describe how you might use a laser pointer to tell which is which.
You are asked to design an optical fiber. Should the refractive index of the core material be larger or smaller than that of the surrounding cladding? For the fastest transmission times, do you want a high or a low refractive index for the core material?
DVD players use a laser with a higher frequency than that of CD players. Why can DVD players read CDs, but CD players cannot read DVDs?
A photographer intends to take a photograph of a country landscape with a large depth of field such that the flowers in the foreground of the picture and a barn in the distance are both in sharp focus. What conditions are more suitable to such a photo, a bright and sunny day or a dim and overcast
Does a camera use a diverging lens or a converging lens? Does a camera produce a real image or a virtual image?
A magnifying glass uses a lens with a focal length of magnitude f= 300 cm. Is f positive or negative?
The largest telescopes are all the reflector variety. Describe and explain two main design considerations in the construction of large-diameter telescopes that favor a reflector over a refractor.
Why does squinting often allow you to read at a distance? For example, even if you forget to wear corrective lenses, forming small slits by squinting your eyes often allows you to read a clock across a room or a sign across a street. Why does squinting help?
When an optometrist determines your eyeglass prescription, she always places a set of “test” lenses in front of your eyes as if they were your real glasses. The optometrist is interested in learning what lenses work best for you, but she is also measuring several other properties of your eyes.
Will the image produced by the contact lenses designed in Section 26.1 (and Eq. 26.7) be upright or inverted? What about the image produced by glasses for a nearsighted person? Explain. flens = 38 cm..... (26.7)
What kind of telescope did Galileo build and use in his studies? Do some investigating and try to find answers to the following questions. (See also Problem 30.) (a) How long was his telescope? (b) What was the total magnification? (c) What was the focal length of the objective lens? (d) What
Is the final image produced by a refracting telescope real or virtual? Explain.
Surgery can be used to correct the vision of a person who is nearsighted. Should the surgeon increase or decrease the curvature of the cornea? What should the surgeon do if the person is farsighted?
If you are nearsighted, should your eyeglasses contain converging lenses or diverging lenses? What if you are farsighted?
Your friend has eyeglasses that make his eyes appear larger than they really are. Is your friend nearsighted or farsighted? Explain.
In Section 26.1, we showed that the angular magnification of a magnifying glass is equal to the ratio of the near-point distance to the focal length of the lens (mθ = sN /f, Eq. 26.14). Hence, by making the focal length sufficiently short, a very large magnification can be achieved in principle.
Will a particular magnifying glass produce the same magnification for any user? Why or why not? If a magnifying glass is marked 5X, what does that imply?
Consider two telescopes, one a reflector and the other a refractor. Assume both telescopes are of equal diameter, are of equal magnification, and have the same focal length. In what ways is the reflector superior to the refractor and vice versa?
Explain why a magnifying glass uses a convex (converging) lens.
To make transistors and other circuit elements that are very small, modern integrated circuits (like those used in a computer) are produced using very high-resolution optical patterning. The process uses a very expensive lens to produce the pattern. If the smallest circuit feature size is 200 nm,
Optometrists quantify the resolution of a patient’s vision using a concept called visual acuity, which is calculated as the inverse of the angular resolution of the eye measured in arc minutes (where 60 arc minutes 5 18) under standard illumination (i.e., in a normal room). The visual acuity of a
An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 20,000 liters of oil have escaped and that
An important application of waves involves using ultrasonic waves (i.e., high-frequency sound waves) to detect flaws in objects such as jet engine turbines and the welds of bridges. Roughly speaking, ultrasonic waves are used to find and image defects inside such solid objects without having to
A very thin soap bubble is floating in air. If the bubble strongly reflects green light (λ = 520 nm), what is the minimum possible thickness of the bubble? Assume the index of refraction of the bubble is n = 1.35.
You want to design an antireflection coating for a lens. You want this coating to work well at two wavelengths, λ1 = 450 nm and λ2 = 650 nm, which you accomplish using two separate layers. One layer uses MgF2 (n = 1.38) and is designed to remove the reflections at wavelength λ1. The second
The Sun appears red when it is on the horizon due to scattering of light by molecules in the atmosphere (Fig. 25.41). The Sun does not appear as reddish in color when it is overhead because the thickness of the atmosphere through which sunlight must travel is smaller when the Sun is overhead than
A challenge astronomers face is that any telescope on the ground must look through many kilometers of air to peer into space. The air is not of uniform refractive index and is also turbulent, which limits the angular resolution of any telescope to approximately 1 arc second (1/3600 of a degree).(a)
(a) A large optical telescope with an aperture of diameter 15 m is used to study the Moon. What is the size of the smallest feature on the Moon that this telescope can resolve using blue light?(b) Calculate the size of the smallest object on Mars that this telescope can resolve. Assume Mars is at
An amateur astronomer’s telescope containing a lens with a diameter of 15 cm is used to study the Moon. What is the smallest object on the Moon that can be resolved with this telescope using blue light? Ignore the effect of the Earth’s atmosphere on the resolution.
A large optical telescope has a mirror with a diameter of 15 m. What is the angular resolution of this telescope when used to form an image with blue light? The diameter of the mirror is the size of the telescope’s “opening” (also called its aperture). Ignore the effect of the Earth’s
Radio telescopes use radio waves (instead of light) to produce images. If radio waves with a frequency of 500 MHz are used together with a radio-wave mirror of diameter 1000 m, what is the best possible angular resolution that can be achieved? Ignore the effect of the Earth’s atmosphere on the
A terrestrial telescope (a “spyglass”) with a diameter of 2.0 cm is attached to a rifle and used for target practice with targets that are 300 m away. What is the smallest feature on the target that can be resolved with this telescope? Assume λ = 400 nm. Ignore the effect of the Earth’s
The camera on a spy satellite has a lens with a diameter of 1.5 m. This satellite is in low-Earth orbit about 2.9 x 105 m above the surface of the Earth. (See Chapter 5, Eq. 5.28.) What is the approximate size of the smallest feature the camera can resolve when taking a picture of something on the
Is the resolution of an optical instrument greater with blue light or with red light? Explain your answer. By approximately what factor are the resolutions different?
Light from a helium–neon laser is incident on a diffraction grating and then illuminates a screen that is 10 m away. If the bright diffraction fringes near θ = 0 are spaced 0.50 m apart, what is the spacing between the slits in the grating?
A grating is illuminated with light from a red laser (λ = 630 nm), producing a diffraction pattern on a screen 3.0 m away in which the first diffraction maximum is spaced 0.55 m from the central diffraction spot. A second laser with an unknown wavelength is then used with the same grating and
You are designing a lecture demonstration on diffraction gratings. You plan to use light from a laser pointer (λ = 630 nm) and shine the light from the grating on the far wall of the lecture room (W = 9.0 m). You want the separation between the central diffraction spot and one of the spots closest
Consider again diffraction from a crystal in Problem 43, but now assume light with λ = 600 nm is used. What is the diffraction angle for the first bright fringe? Your answer explains why visible light cannot be used in diffraction experiments with crystals.
The atomic planes in a crystal are spaced d = 0.50 nm apart. These planes are used in a diffraction experiment with X-rays with λ = 0.05 nm. Assume the bright fringes in the diffraction pattern are at the same angles as for a grating with slits with the same value of d. What are the diffraction
Light from two laser pointers with wavelengths 630 nm (red light) and 470 μm (blue light) is incident on a diffraction grating with a slit spacing of 10 mm, and the diffracted light illuminates a screen 2.2 m away. What is the distance on the screen between the first red fringe and the first blue
A sodium lamp produces yellow light with wavelengths λ and λ + Δλ, where λ 589.00 nm and Δλ = 0.59 nm. This light is incident on a diffraction grating with a slit spacing of 15μm, and the diffracted light illuminates a screen 2.5 m away. What is the distance on the screen between the
A diffraction grating is a square 1.0 cm on a side and contains 3000 slits. What is the angle of the first intensity maximum in the diffraction pattern with blue light (λ = 450 nm)?
The slits in a diffraction grating are spaced 25 μm apart. What is the diffraction angle for the second bright fringe away from θ = 0 with red light (λ = 600 nm)?
A helium–neon laser (λ = 630 nm) is used in a single-slit experiment with a screen 3.0 m away from the slit. If the slit is 0.25 mm wide, what is the width of the central bright fringe on the screen? Measure this width using the locations where there is destructive interference.
Light with λ = 550 nm passes through a single slit and then illuminates a screen 2.0 m away. If the distance on the screen from the first dark fringe to the center of the interference pattern is 5.5 mm, what is the width of the slit?
A slit with a width 0.15 mm is located 10 m from a screen. If light with l 450 nm is passed through this slit, what is the distance between the central bright fringe and the third dark fringe on the screen?
A doorway acts as a single slit for light that passes through it, but a doorway is much larger than the wavelength of visible light, so the diffraction angles are very small. Estimate the angle of the 10th diffraction minimum for a typical doorway if light from a red laser pointer (λ = 630 nm)
Red light (λ = 600 nm) is diffracted by a single slit, and the first intensity minimum (the first dark fringe) occurs at u 6.9°. What is the width of the slit?
Two narrow slits are used to produce a double-slit interference pattern with monochromatic light. It is found that the third bright fringe from the center with blue light (λ1 = 420 nm) occurs at the same place on the screen as the second bright fringe with the light of an unknown wavelength λ2.
A Young’s double-slit interference experiment gives bright fringes separated by 2.5 cm on a screen when the experiment is performed in air. The entire apparatus is then placed under water (n = 1.33). What is the new spacing between bright fringes? Assume the fringes are near the center of the
Two narrow slits are used to produce a double-slit interference pattern with monochromatic light (λ = 450 nm). The slits are separated by 0.90 mm, and the interference pattern is projected onto a screen 7.5 m away from the slits.(a) What is the distance between two nearby bright fringes on the
Two narrow slits are used to produce a double-slit interference pattern with monochromatic light. The slits are separated by 0.90 mm, and the interference pattern is projected onto a screen 9.5 m away from the slits. The central bright fringe is at a certain spot on the screen. Using a ruler with
Two slits are separated by 0.35 mm and are used to perform a double-slit experiment with a screen 1.5 m away from the slits. If the distance between a dark region and the nearest bright spot on the screen is 1.0 mm, what is the wavelength?
Monochromatic light (λ = 500 nm) passes through two slits and onto a screen 2.5 m away. (a) If two nearby bright fringes are separated by 12 mm, what is the slit spacing? (b) If the slit spacing is reduced by a factor of three, what is the new distance between bright fringes?
In Problem 26, you were told to assume the speakers could be treated as point sources. Which of the following statements justifies this assumption?(a) Small speakers could be much smaller than the wavelength of the sound waves.(b) The speakers could be larger than the wavelength but smaller than
Two small stereo speakers are 2.5 m apart and act as a double-slit interference experiment with sound waves. If the opposite wall of the room is 5.5 m away and the sound frequency is 1.5 kHz, what is the distance between the two interference maxima nearest the center of the wall? Assume the
A double-slit interference experiment is performed with two very narrow slits separated by 0.15 mm. The experiment uses red light with a wavelength of 600 nm and projects the interference pattern onto a screen 7.5 m away from the slits.(a) What is the distance between two nearby bright fringes on
Single-slit diffraction can be observed with any type of electromagnetic wave (not just light). Suppose you want to make a diffraction slit whose width is five times larger than the wavelength for the following cases. How wide would the slit be? (a) A radio wave for your favorite FM station (f =
Two glass plates are arranged as in Figure 25.12 so that light reflected from the bottom surface of the top plate interferes with light reflected from top surface of the bottom plate. As one moves along the x-axis, the total reflected intensity alternates between bright and dark fringes. If there
A very thin sheet of glass (n =1.55) floats on the surface of water (n = 1.33). When illuminated with white light at normal incidence, the reflected light consists predominantly of the wavelengths 560 nm and 400 nm. How thick is the glass?
An extremely thin film of soapy water (n = 1.35) sits on top of a flat glass plate with n 1.50. The soap film has a red color when viewed at normal incidence. What is the thickness of the film? (λred = 600 nm.)
A Michelson interferometer is used to check the length of a “standard” platinum meterstick. The interferometer is operated with light from a specially constructed helium–neon laser, which gives red light with λ = 632.99139822 nm.(a) The standard meterstick is placed next to one of the
Consider a Michelson interferometer operated with light from a sodium lamp with λNa = 589 nm. Suppose the interferometer is used to check the accuracy of a meter stick by moving one of the mirrors a distance of precisely 1.00 m (as determined by the meter stick) and counting bright fringes as they
Consider a Michelson interferometer that uses a sodium lamp as its source. A sodium lamp gives a large intensity at two wavelengths, 589.00 nm and 589.59 nm, in the yellow range of the visible spectrum. For such a light source, the intensity pattern of the interferometer is just the sum of the
Both arms of a Michelson interferometer are enclosed in pipes so that the air can be removed from the regions between the mirrors and the beam splitter. There is initially a vacuum in both regions, and the mirrors are the same distance from the beam splitter. Air is then let into one of the pipes,
Suppose the wavelength in Problem 10 is increased by a factor of 1.2. How many dark fringes would now be found when the mirror moves the same distance?
Coherent sound waves are emitted from points P1 and P2 in Figure P25.6. The waves have a wavelength λ = 1.5 m. (a) Find the point on the +x axis nearest the origin at which the waves interfere constructively. (b) Find the point on the +x axis nearest the origin at which the waves interfere
The detection point in Problem 4 is moved so that it is 1.50000 mm from one source and 1.50150 mm from the other. If the two waves interfere destructively, what is a possible value for the wavelength? Assume the light is visible light and keep three significant figures in your calculation.
Two sources produce coherent light waves that come together at a detector located 1.50000 mm from one source and 1.50500 mm from the other. If the two waves interfere constructively, what is a possible value for the wavelength? Assume the light is visible light.
Sound waves with a wavelength of 0.25 m are emitted coherently (i.e., in phase with each other) from two sources. These waves are found to interfere constructively at a point P that is 1.60 m from one of the sources. What is the distance from P to the other source? There is more than one correct
Light waves are emitted coherently from two sources and detected at a spot equidistant from the two sources. Do these waves interfere constructively or destructively at this spot?
Figure 25.20 shows the intensity pattern produced in a double-slit interference pattern with two very narrow slits. Suppose one of the slits is covered so that light can only pass through one slit. Sketch what the new intensity pattern would look like.
Which single-slit diffraction experiment will give the widest central bright fringe,(a) a 900-nm slit with the light of wavelength 500 nm.(b) a 600-nm slit with the light of wavelength 450 nm?
The star in the bottom of the Northern Cross asterism is actually a binary pair. The photo graph in Figure Q25.14 came from a telescope with a mirror 10 inches in diameter. Which feature of the telescope is more important in enabling it to resolve the pair when your eye sees them as one point of
In Section 25.2, we assumed the Michelson interferometer was operated with monochromatic light (light of a single wavelength). Suppose a source of white light is used instead. It is also possible to have constructive interference and hence a bright fringe with white light. What value(s) of the path
Design an experiment in which light from a helium-neon laser (λ = 630 nm) can be used to measure(a) the width of a single slit(b) the distance between two nearby slits.
Constructive interference occurs when the crests of two coherent waves overlap (Fig. 25.1B). What happens when the troughs of two coherent waves overlap? Is interference constructive or destructive? Explain.
Explain how a thin coating on a lens (called an antireflection coating) can reduce the amount of reflected light by using destructive interference. Most expensive lenses have these coatings.
Green light is used to make a single-slit diffraction pattern with a particular slit. If the same slit is used with red light, will the width of the central bright fringe be wider or narrower?
How does a double-slit interference pattern change when the following changes are made? Do the interference fringes become closer together or farther apart? Explain your answers. (a) The two slits are brought closer together. (b) The two slits are moved farther apart. (c) The wavelength is
Yellow light is used to make a double-slit interference pattern with two very narrow slits. If the same slits are used with blue light, will the separation between two adjacent bright fringes be larger or smaller?
Explain why two light waves can interfere only if they are coherent.
If a soap film suspended in air is extremely thin, what color will it be when viewed in reflected light?
Why don’t you observe interference between light waves produced by two lightbulbs?
Is it possible for light of two different colors to exhibit constructive or destructive interference? Explain.
Two light signals are traveling through a piece of crown glass of length 30 km (it might be an optical fiber.) One of the signals uses red light, and the other uses blue light.(a) If the signals travel straight through the glass with no reflections from the surfaces, which signal arrives first, the
A monster is 10 m in front of a convex mirror and appears with a magnification of 0.50. What is the radius of curvature of the mirror?
Some creative amateur astronomers have been known to improve their view of the night sky by wearing scuba gear and observing the sky from the bottom of a swimming pool. Looking up from the bottom of a swimming pool, you are able to see a wider angle of the sky with a pool full of water than when
Suppose you use the pinhole camera described in Problem 106 to photograph the Sun during an eclipse. Determine the size of the image of the Sun. Repeat the calculation for the Moon.
The earliest cameras were simply light-tight boxes with a very small hole in one side of the box. By uncovering the pinhole for a brief period of time, light from an object could pass through the hole, exposing a photographic plate (film) on the inside of the box. Later versions of this type of
An overhead projector produces an image of an object (transparency) on a distant screen by using a light source, a plane mirror, and a converging lens (f = 50 cm). The distance between the lens and the mirror is 15 cm.(a) If you wish to project a focused image on a screen 3.0 m away from the lens,
A birdwatcher observes a hummingbird at a distance of 10 m through a simple eyepiece (converging lens) of focal length 25 cm (Fig. P24.101). As the hummingbird flies away at a speed of 2.5 m/s, how fast does the image move? Does the image move toward or away from the lens?
A rock is dropped in a large tank of benzene and sinks to the bottom of the tank. If the apparent depth of the rock as viewed directly from above is 35 cm, what is the actual depth of the rock?
A laser beam strikes in the center of one end of a long, thin glass plate that has an index of refraction of 1.5 as shown in Figure P24.94. Determine the number of internal reflections the beam undergoes before it exits the plate at the other end.
Suppose a ray of light is incident on three stacked layers of glass with different indices of refraction as shown in Figure P24.92. If the ray enters from air, what is the angle θ3?
Prior to the development of the digital camera, the 35-mm film camera was the norm. The designation “35 mm” refers to the size of the film (screen) on which the image is formed. Suppose you wish to use one of these cameras to photograph a 10-m-tall tree that is 30 m away and have the tree’s
A slide projector uses a converging lens to project images on a screen 4.0 m away. If the distance between the slide (image) and the lens is 5.0 cm, what are(a) the focal length of the lens(b) the magnification of the image?
Brewster’s angle (see Problem 87) for one face of a particular prism is found to be 65°. What is the index of refraction of the prism?
Compare the forms of the lens maker’s formulas in Equation 24.32 and Problem 85 and devise a formula for a lens that has one concave surface and one convex surface.
Consider the lens in Problem 83. An object is placed 95 cm in front of the lens and is illuminated with white light. Chromatic aberration causes the image formed with blue light to be at a different position than the red image. How far apart are the two images?
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