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physics
light and optics

Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions

Lenses used in eyeglasses, whether converging or diverging, are always designed so that the middle of the lens curves away from the eye, like the center lenses of Figure 36.27a and b. Why?
Which glasses in Figure Q36.19 correct nearsightedness and which correct farsightedness?
A child tries on either his hyperopic grandfather’s or his myopic brother’s glasses and complains that “everything looks blurry.” Why do the eyes of a person wearing glasses not look blurry? (See Figure Q36.19.)
Consider a spherical concave mirror, with the object located to the left of the mirror beyond the focal point. Using ray diagrams show that the image moves to the left as the object approaches the focal point.
In a Jules Verne novel, a piece of ice is shaped to form a magnifying lens to focus sunlight to start a fire. Is this possible?
The f -number of a camera is the focal length of the lens divided by its aperture (or diameter). How can the f –number of the lens be changed? How does changing this number affect the required exposure time?
A solar furnace can be constructed by using a concave mirror to reflect and focus sunlight into a furnace enclosure. What factors in the design of the reflecting mirror would guarantee very high temperatures?
One method for determining the position of an image, either real or virtual, is by means of parallax. If a finger or other object is placed at the position of the image, as shown in Figure Q36.25, and the finger and image are viewed simultaneously (the image is viewed through the lens if it is
Figure Q36.26 shows a lithograph by M. C. Escher titled Hand with Reflection Sphere (Self-Portrait in Spherical Mirror). Escher had this to say about the work: €œThe picture shows a spherical mirror, resting on a left hand.But as a print is the reverse of the original drawing on stone, it
You can make a corner reflector by placing three flat mirrors in the corner of a room where the ceiling meets the walls. Show that no matter where you are in the room, you can see yourself reflected in the mirrors— upside down.
A converging lens of short focal length can take light diverging from a small source and refract it into a beam of parallel rays. A Fresnel lens, as shown in Figure 36.29, is used for this purpose in a lighthouse. A concave mirror can take light diverging from a small source and reflect it into a
Why can you hear around corners, but not see around corners?
Holding your hand at arm’s length, you can readily block sunlight from reaching your eyes. Why can you not block sound from reaching your ears this way?
Observe the shadow of your book when it is held a few inches above a table with a small lamp several feet above the book. Why is the shadow somewhat fuzzy at the edges?
Knowing that radio waves travel at the speed of light and that a typical AM radio frequency is 1 000 kHz while an FM radio frequency might be 100 MHz, estimate the wavelengths of typical AM and FM radio signals. Use this information to explain why AM radio stations can fade out when you drive your
Describe the change in width of the central maximum of the single-slit diffraction pattern as the width of the slit is made narrower.
John William Strutt, Lord Rayleigh (1842€“1919), is known as the last person to understand all of physics and all of mathematics. He invented an improved foghorn. To warn ships of a coastline, a foghorn should radiate sound in a wide horizontal sheet over the ocean€™s surface.
Featured in the motion picture M*A*S*H (20th Century Fox, Aspen Productions, 1970) is a loudspeaker mounted on an exterior wall of an Army barracks. It has an approximately rectangular aperture. Its design can be thought of as based on Lord Rayleigh’s foghorn trumpet, described in Question 6.
Assuming that the headlights of a car are point sources, estimate the maximum distance from an observer to the car at which the headlights are distinguishable from each other.
A laser beam is incident at a shallow angle on a machinist’s ruler that has a finely calibrated scale. The engraved rulings on the scale give rise to a diffraction pattern on a screen. Discuss how you can use this technique to obtain a measure of the wavelength of the laser light.
When you receive a chest x-ray at a hospital, the rays pass through a series of parallel ribs in your chest. Do the ribs act as a diffraction grating for x-rays?
Certain sunglasses use a polarizing material to reduce the intensity of light reflected from shiny surfaces. What orientation of polarization should the material have to be most effective?
During the “day” on the Moon (when the Sun is visible), you see a black sky and the stars can be clearly seen. During the day on the Earth, you see a blue sky with no stars. Account for this difference.
You can make the path of a light beam visible by placing dust in the air (perhaps by clapping two blackboard erasers in the path of the light beam). Explain why you can see the beam under these circumstances. In general, when is light visible?
Is light from the sky polarized? Why is it that clouds seen through Polaroid glasses stand out in bold contrast to the sky?
If a coin is glued to a glass sheet and this arrangement is held in front of a laser beam, the projected shadow has diffraction rings around its edge and a bright spot in the center. How is this possible?
How could the index of refraction of a flat piece of dark obsidian glass be determined?
A laser produces a beam a few millimeters wide, with uniform intensity across its width. A hair is stretched vertically across the front of the laser to cross the beam. How is the diffraction pattern it produces on a distant screen related to that of a vertical slit equal in width to the hair? How
A radio station serves listeners in a city to the northeast of its broadcast site. It broadcasts from three adjacent towers on a mountain ridge, along a line running east and west. Show that by introducing time delays among the signals the individual towers radiate, the station can maximize net
What is the necessary condition on the path length difference between two waves that interfere? (a) Constructively and (b) Destructively?
Explain why two flashlights held close together do not produce an interference pattern on a distant screen.
If Young’s double-slit experiment were performed under water, how would the observed interference pattern be affected?
In Young’s double-slit experiment, why do we use monochromatic light? If white light is used, how would the pattern change?
A simple way to observe an interference pattern is to look at a distant light source through a stretched handkerchief or an opened umbrella. Explain how this works.
A certain oil film on water appears brightest at the outer regions, where it is thinnest. From this information, what can you say about the index of refraction of oil relative to that of water?
As a soap bubble evaporates, it appears black just before it breaks. Explain this phenomenon in terms of the phase changes that occur on reflection from the two surfaces of the soap film.
If we are to observe interference in a thin film, why must the film not be very thick (with thickness only on the order of a few wavelengths)?
A lens with outer radius of curvature R and index of refraction rests on a flat glass plate. The combination is illuminated with white light from above and observed from above. Is there a dark spot or a light spot at the center of the lens? What does it mean if the observed rings are noncircular?
Why is the lens on a good-quality camera coated with a thin film?
Why is it so much easier to perform interference experiments with a laser than with an ordinary light source?
Suppose that reflected white light is used to observe a thin transparent coating on glass as the coating material is gradually deposited by evaporation in a vacuum. Describe color changes that might occur during the process of building up the thickness of the coating.
In our discussion of thin-film interference, we looked at light reflecting from a thin film. What If? Consider one light ray, the direct ray, which transmits through the film without reflecting. Consider a second ray, the reflected ray that transmits through the first surface, reflects from the
Suppose you are watching television by connection to an antenna rather than a cable system. If an airplane flies near your location, you may notice wavering ghost images in the television picture. What might cause this?
A 55-mm- focal-length lens has f-stops ranging from f /1.4 to f /22. What is the corresponding range of lens diaphragm diameters?
A television camera lens has a 14-cm focal length and a lens diameter of 6.0 cm. what is its f-number?
A light meter reports that a camera setting of 1/250 s at f /5.6 will give a correct exposure. But the photographer wishes to use f /11 to increase the depth of field. What should the shutter speed b?
A properly exposed photograph is taken at f / 16 and 1/60 s. what lens opening would be required if the shutter speed were 1/1000 s?
If an f = 135-mm telephoto lens is designed to cover object distances from 1.2 m to 00, over what distance must the lens move relative to the plane of the film?
A 200-mm-focal-length lens can be adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances can it be adjusted?
A nature photographer wishes to photograph a 28-m-tall tree from a distance of 58 m. what focal-length lens should be used if the image is to fill the 24-mm height of the film?
A ‘’pinhole’’ camera uses a tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider two point objects 2.0cm apart that are 1.0m from a 1.0-mm –diameter pinhole. Show that on a piece of film
Suppose that a correct exposure is 1/250 s at f /11. Under the same conditions, what exposure time would be needed for a pinhole camera (problem 8) if the pinhole diameter is 1.0 mm and the film is 7.0 cm from the hole?
A human eyeball is about 2.0 cm long, and the pupil has a maximum diameter of about 8.0mm. What is the “speed” of this lens?
If the nearsighted person in example 25-6 wore contact lenses corrected for the far point (= 00), show that the near point would be 41 cm. (would glasses be better in this case?)
Reading glasses of what power are needed for a person whose near point is 115 cm, so that he can read a computer screen at 55 cm? Assume a lens- eye distance of 1.8 cm.
A person has a far point of 14 cm. what power glasses would correct this vision if the glasses were placed 2.0 cm from the eye? What power contact lenses, placed on the eye, would be person need?
A person struggles to read by holding a book at arm’s length, a distance of 45 cm away (= near point). What power of reading glasses should be prescribed for him, assuming they will be placed 2.0 cm from the eye and he wants to read at the normal near point of 25 cm?
A person’s left eye is corrected by a -3.50-diopter lens, 2.0 cm from the eye.(a) Is this person’s left eye near- or farsighted?(b) What is this eye’s far point without glasses?
A person’s right eye can see objects clearly only if they are between 25 cm and 75 cm away,(a) What power of contact lens is required so that object far away is sharp?(b) What will be the near point with the lens in place?
About how much longer is the nearsighted eye in example 25-6 than the 2.0 cm of a normal eye?
One lens of a nearsighted person’s eyeglasses has a focal length of -22.0 cm, and the lens is 81.8 cm from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?
What is the focal length of the eye-lens system when viewing an object?(a) At infinity, and (b) 33 cm from the eye? Assume that the lens-retina distance is 2.0 cm.
A nearsighted person has near and far points of 10.0 and 20.0 cm, respectively. If she puts on contact lenses with power P = -4.00 D. what are her new near and far points?
What is the magnification of a lens used with a relaxed eye if its focal length is 12cm?
What is the focal length of a magnifying glass of 3.5X magnification for a relaxed normal eye?
A magnifier is rated at 2.5X for a normal eye focusing on an image at the near point.(a) What is its focal length?(b) What is its focal length if the 2.5X refers to a relaxed eye?
Sherlock Holmes is using a 9.00-cm-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?
A 3.30-mm-wide beetle is viewed with a 9.50-cm-focal-length lens. A normal eye views the image at its near point. Calculate(a) The angular magnification,(b) The width of the image, and(c) The object distance from the lens.
A small insect is placed 5.55 cm from a +6.00-cm –focal-length lens. Calculate(a) The position of the image, and(b) The angular magnification.
A magnifying glass with a focal length of 8.5 cm is used to read print placed at a distance of 7.5 cm. calculate(a) The position of the image;(b) The angular magnification.
A magnifying glass is rated at 3.0X for a normal eye that is relaxed. What would be the magnification of this lens for a relax eye whose near point is(a) 55 cm, and(b) 16 cm ? Explain the differences.
What is the magnification of an astronomical telescope whose objective lens has a focal length of 76 cm and whose eyepiece has a focal length of 2.8 cm? What is the overall length of the telescope when adjusted for a relaxed eye?
The overall magnification of an astronomical telescope is desired to be 25X. If an objective of 78-cm focal length is used, what must be the focal length of the eyepiece? What is the overall length of the telescope when adjusted for used by the relaxed eye?
An 8.0X binocular has 2.8-cm-focal-length eyepieces. What is the focal length of the objective lenses?
An astronomical telescope has an objective with focal length 85 cm and a +35-D eyepiece. What is the total magnification?
An astronomical telescope has its two lenses spaced 75.2 cm apart. If the objective lens has a focal length of 74.5 cm, what is the magnification of this telescope? Assume a relaxed eye.
A Galilean telescope adjusted for a relaxed eye is 32.8 cm long. If the objective lens has a focal length of 36.0 cm, what is the magnification?
What is the magnifying power of an astronomical telescope using a reflective mirror whose radius of curvature is 6.0 m and an eyepiece whose focal length is 3.2 cm?
The moon’s image appears to be magnified 120X by a reflecting astronomical telescope with an eyepiece having a focal length of 3.2 cm. what are the focal length and radius of curvature of the main (objective) mirror?
A 170X astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.25 m apart. What is the focal length of each lens?
A reflecting telescope (Fig. 25-21b) has a radius of curvature of 3.0 m for its object mirror and a radius of curvature of -1.50 m for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the photographic film to record the image
A microscope uses an eyepiece with a focal length of 1.40 cm using a normal eye with a final image at infinity, the tube length is 17.5 cm and the focal length of the objective length is 0.65 cm. What is the magnification of the microscope?
A 620X microscope uses a 0.40-cm-focal-length objective lens. If the tube length is 17.5 cm, what is the focal length of the eyepiece? Assume a normal eye and that the final image is at infinity.
A 17-cm-long microscope has an eyepiece with a focal length of 2.5 cm and an objective with a focal length of 2.5 cm. what is the approximate magnification?
A microscope has a 12.0X eyepiece and a 59.0X objective lens 20.0 cm apart. Calculate (a) The total magnification,(b) The focal length of each lens, and(c) Where the object must be for a normal relaxed eye to see it in focus.
A microscope has a 1.8-cm-focal-length eyepiece and a 0.80-cm objective lens. Assuming a relaxed normal eye, calculate(a) The position of the object if the distance between the lenses is 16.0 cm, and(b) The total magnification.
Repeat problem 43 assuming that the final image is located 25 cm from the eyepiece (near point of a normal eye).
The eyepiece of a compound microscope has a focal length of 2.70 cm, and the objective lens has f =0.740 cm, if an object is placed 0.790 cm from the objective lens, calculate(a) The distance between the lenses when the microscope is adjusted for a relaxed eye, and(b) The total magnification.
An achromatic lens is made of two very thin lenses, placed in contact, that have focal lengths of f1 = -28 cm and f2 = +23(a) Is the combination converging or diverging?(b) What is the net focal length?
Let€™s examine spherical aberration in a particular situation. A planoconvex lens of index of refraction 1.50 and radius of curvature R = 12.0cm is shown fig,25-48 consider an incoming ray parallel to the principal axis and a high above it as shown determine the distance d, from the flat
What is the angular resolution limit (degrees) set by diffraction for the 100-in. (254-cm mirror diameter) Mt. Wilson telescope (λ =550 nm)?
Suppose that you wish to construct a telescope that can resolve features 7.0km across on the moon.383, 000 km away. You have a 2.0-m-focal-length objective lens whose diameter is 11.0cm. what focal –length eyepiece is needed if your eye can resolution objects 0.10mm apart at a distance of 25cm?
The normal lens on a 35-mm camera has a focal length of 50.0mm. Its apertures diameter varies from a maximum of 25mm (f /2) to maximum of 3.0 mm (f /16). Determine the resolution limit set by diffraction for f /2 and f /16, specify as the1 number of lines per millimeter resolved on the film, take
Two stars 15 light-years away are barely resolved by a 55-cm (mirror diameter) telescope. How far apart are the stars? Assume λ = 550 nm and that the resolution is limited by diffraction.
(a) How far away can a human eye distinguish two ear headlights 2.0 m apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 mm and a wavelength of 550 nm.(b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction
The earth and moon are separated by about 400 X 106 m. when mars is 8 X 1010 m from earth, could a person standing on mars resolve the earth and its moon as two separate objects without a telescope? Assume a pupil diameter of 5 mm and λ = 550 nm.
X-rays of wavelength 0.133 nm fall on a crystal whose atoms, lying in planes, are spaced 0.280 nm apart. At what angle Φ (relative to the surface, Fig.25-37) must the X-rays be directed if the first diffraction maximum is to be observed?
X-rays of wavelength 0.0973 nm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an angle of 23.4° relative to the crystal surface. What is the spacing between crystal planes?
First-order Bragg diffraction is observed at 25.2° related to the crystal surface, with spacing between atoms of 0.24 nm.(a) At what angle will second order be observed?(b) What is the wavelength of the X-rays?
(a) Suppose for a conventional X-ray image that the X-ray beam consists of parallel rays, what would be the magnification of the image?(b) Suppose, instead, the X-rays come from a point source (as in Fig. 25-41) that is 15 cm in front of a human body 25 cm thick, and the film is pressed against the

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