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physics
light and optics

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

A salesman tries to sell you an optic fiber that claims to give linearly polarized light when light is totally internally reflected off the fiber–air interface. (a) Would you buy it? Explain. (b) If total internal reflection occurs at an angle of 42°, what would be the polarizing (Brewster)
Three parallel slits of width w have a slit separation of d, where d = 3w. (a) Will you be able to see all the interference maxima? Explain. (b) If not, which interference maxima will be missing?
Show that when the reflected light is completely polarized, the sum of the angle of incidence and the angle of refraction is equal to 90o.
The critical angle for a certain plastic and air interface is 39o. If the angle of incidence is adjusted so the reflected light has maximum polarization, what would be the angle of refraction?
A diver under water is looking at the overhead Sun through a diffraction grating that has 5000 lines/cm. What is the highest complete spectrum order that can be seen by the diver?
(a) If the wavelength used in a double-slit experiment is decreased, the distance between adjacent maxima will (1) increase, (2) decrease, (3) remain the same. Explain. (b) If the separation between the two slits is 0.20 mm and the adjacent maxima of the interference pattern on a screen 1.5 m away
In a double-slit experiment using monochromatic light, a screen is placed 1.25 m away from the slits, which have a separation distance of 0.0250 mm. The position of the third-order maximum is 6.60 cm from the center of the central maximum. Find (a) The wavelength of the light and (b) The position
In a double-slit experiment with monochromatic light and a screen at a distance of 1.50 m from the slits, the angle between the second-order maximum and the central maximum is 0.0230 rad. If the separation distance of the slits is 0.0350 mm, what are (a) The wavelength and color of the light and
What are the main differences among the following refracting telescopes: an astronomical telescope, a Galilean telescope, and a terrestrial telescope?
Why are chromatic and spherical aberrations important factors in refracting telescopes, but not in reflecting telescopes?
A reflecting telescope with a large objective mirror can collect more light from stars than a reflecting telescope with a smaller objective mirror. What other advantage is gained with a large mirror? Explain.
In order to observe fine details of small objects in a microscope, should you use blue light or red light?
Several beverages, such as root beer, develop a “head” of foam when poured into a glass. Why is the foam generally white or light colored, whereas the liquid is dark?
A fifty-year-old person has a far point of 20 m and near point of 45 cm. What type of corrective glasses would be necessary to correct this person’s vision?
A person with nearsightedness wishes to switch from regular glasses to contact lenses. Should the contact lenses have a stronger or a weaker prescription than the glasses? Explain.
With an object at the focal point of a magnifying glass, the magnification is given by m = (25 cm) / f (Eq. 25.4). According to this equation, the magnification could be increased indefinitely by using lenses with shorter focal lengths. Why, then, are compound microscopes needed?
If you are given two lenses with different focal lengths, how would you decide which should be used as the objective and which should be used as the eyepiece for a telescope? Explain.
What are the powers of (a) A converging lens of focal length 20 cm and (b) A diverging lens of focal length – 50cm?
A nearsighted student wears contact lenses to correct for a far point that is 4.00 m from her eyes. When she is not wearing her contact lenses, her near point is 20 cm. What is her near point when she is wearing her contacts?
A nearsighted woman has a far point located 2.00 m from one eye. (a) If a corrective lens is worn 2.00 cm from the eye, what would be the necessary power of the lens for her to see distant objects? (b) What would be the necessary power if a contact lens were used?
A nearsighted man wears eyeglasses whose lenses have a focal length of –0.255. How far away is his far point?
An eyeglass lens with a power of + 2.8 D allows a far-sighted person to read a book held at a distance of 25 cm from her eyes. At what distance must she hold the book to read it without glasses?
A college professor can see objects clearly only if they are between 70 and 500 cm from her eyes. Her optometrist prescribes bifocals (Fig. 25.23) that enable her to see distant objects through the top half of the lenses and read students€™ papers at a distance of 25 cm through the lower
A senior citizen wears bifocals (Fig. 25.23) in which the top half of the lens has a focal length of – 0.850 and the bottom half of the lens has a focal length of + 0.500. What are this person’s near point and far point?
A certain man has a far point of 150 cm. (a) What power must contact lenses have to allow him to see distant objects clearly? (b) If he is able to read a newspaper at 25 cm while wearing his contacts, is his near point less than 25 cm? If so, what is it? (c) Give an approximation of the man’s
A middle-aged man starts to wear eyeglasses with lenses of +2.0 D that allow him to read a book held as close as 25 cm. Several years later, he finds that he must hold a book no closer than 33 cm to read it clearly with the same glasses, so he gets new glasses. What is the power of the new lenses?
Bifocal glasses are used to correct both nearsightedness and farsightedness at the same time (Fig. 25.23). If the near points in the right and left eyes are 35.0 cm and 45.0 cm, respectively, and the far point is 220 cm for both eyes, what are the powers of the lenses prescribed for the glasses?
Using the small-angle approximation, compare the angular sizes of a car 1.5 m in height when viewed from distances of (a) 500 m and (b) 1050 m.
A person is prescribed with contact lenses that have powers of – 3.0 D. What type of lenses are these? What is the lenses’ focal length?
An object is placed 10 cm in front of a converging lens with a focal length of 18 cm. What are (a) The lateral magnification and (b) The angular magnification?
A biology student uses a converging lens to examine the details of a small insect. If the focal length of the lens is 12 cm, what is the maximum angular magnification?
A converging lens can give a maximum angular magnification of 4.0 x. What is the focal length of the lens?
When viewing an object with a magnifying glass whose focal length is 10 cm, a student positions the lens so that there is minimum eyestrain. What is the observed magnification?
A physics student uses a converging lens with a focal length of 14 cm to read a small measurement scale. (a) Maximum magnification is achieved if the image is at (1) the near point, (2) infinity, (3) the far point. Explain. (b) What are the magnifications when the image is at the near point and
A detective wants to achieve maximum magnification when looking at a fingerprint with a magnifying glass. (a) He should use a lens with (1) a long focal length, (2) a short focal length, (3) a larger size. Explain. (b) If he uses lenses of focal length + 28 cm and + 40 cm, what are the maximum
What is the maximum magnification of a magnifying glass with a power of + 3.0 D for (a) A person with a near point of 25 cm and (b) A person with a near point of 10 cm?
If a magnifying glass gives an angular magnification of 1.5 x when viewed with relaxed eyes, what is the power of the lens?
A compound microscope has an objective with a focal length of 4.00 mm and an eyepiece with a magnification of 10.0x. If the objective and eyepiece are 15.0 cm apart, what is the total magnification of the microscope?
A compound microscope has a distance of 15 cm between lenses and an objective with a focal length of 8.0 mm. What power should the eyepiece have to give a total magnification of – 360x?
The far point of a certain nearsighted person is 90 cm. (a) Which type of contact lenses, (1) converging, (2) diverging, or (3) (2) diverging, or (3) bifocal, should an optometrist prescribe to enable the person to see more distant objects clearly? Explain. (b) What would the power of the lenses
The focal length of the objective lens of a compound microscope is 4.5 mm. The eyepiece has a focal length of 3.0 cm. If the distance between the lenses is 18 cm, what is the magnification of a viewed image?
A compound microscope has an objective lens with a focal length of 0.50 cm and an eyepiece with a focal length of 3.25 cm. The separation distance between the lenses is 22 cm. (a) What is the total magnification? (b) Compare (as a percentage) the total magnification with the magnification of the
The lenses used in a compound microscope have powers of + 100 D and + 50 D. If a total magnification of is desired, what should be the distance between the two lenses?
Two lenses of focal length 0.45 cm and 0.35 cm are available for a compound microscope using an eyepiece of focal length of 3.0 cm, and the distance between the lenses has to be 15 cm. (a) Which lens should be used as the objective: (1) the one with the longer focal length, (2) the one with the
A – 150 x microscope has an eyepiece whose focal length is 4.4 cm. If the distance between the lenses is 20 cm, find the focal length of the objective.
A specimen is 5.0 mm from the objective of a com-pound microscope that has a lens power of + 250 D. What must be the magnifying power of the eyepiece if the total magnification of the specimen is – 100 x?
A lens with a power of + 10 D is used as a simple microscope. (a) For the image of an object to be seen clearly, can the object be placed infinitely close to the lens, or is there a limit on how close it can be? Explain. (b) Calculate how close an object can be brought to the lens. (c) What is
A modern microscope is equipped with a turret that has three objectives with focal lengths of 16 mm, 4.0 mm, and 1.6 mm and interchangeable eyepieces of 5.0 x and 10x. A specimen is positioned such that each objective produces an image 150 mm from the objective. (a) Which objective and eyepiece
Find the magnification and length of a telescope whose objective has a focal length of 50 cm and whose eyepiece has a focal length of 2.0 cm.
An astronomical telescope has an objective and an eyepiece whose focal lengths are 60 cm and 15 cm, respectively. What are the telescope’s (a) Magnifying power and (b) Length?
A certain farsighted person has a near point of 50 cm. (a) Which type of contact lenses, (1) converging, (2) diverging, or (3) (2) diverging, or(3) bifocal, should an optometrist prescribe to enable the person to see clearly objects as close as 25 cm? Explain. (b) What is the power of the lenses,
An astronomical telescope has an eyepiece with a focal length of 10.0 mm. If the length of the tube is 1.50 m, (a) What is the focal length of the objective? (b) What is the angular magnification of the telescope when it is focused for an object at infinity?
A telescope has an angular magnification of – 50 x and a barrel 1.02 m long. What are the focal lengths of the objective and the eyepiece?
A terrestrial telescope has three lenses: an objective, an erecting lens, and an eyepiece. (a) Does the erecting lens (1) increase the magnification, (2) increase the physical length of the telescope, (3) decrease the magnification, or (4) decrease the physical length of the telescope? Explain.
A terrestrial telescope uses an objective and eyepiece with focal lengths of 42 cm and 6.0 cm, respectively. (a) What should the focal length of the erecting lens be if the overall length of the telescope is to be 1.0 m? (b) What is the magnification of the telescope for an object at infinity?
An astronomical telescope uses an objective of power +2.00 D. If the length of the telescope is 52 cm, (a) What is the focal length of the eyepiece? (b) What is the angular magnification of the telescope?
You are given two objectives and two eyepieces and are instructed to make a telescope with them. The focal lengths of the objectives are 60.0 cm and 40.0 cm, and the focal lengths of the eyepieces are 0.90 cm and 0.80 cm. (a) Which lens combination would you pick if you want to have maximum
(a) For a given wavelength, a wider single slit will give (1) a greater, (2) a smaller, (3) the same minimum angle of resolution as a narrower slit, according to the Rayleigh criterion. (b) What are the minimum angles of resolution for two point sources of red light (λ = 680 nm) in the
The minimum angle of resolution of the diffraction patterns of two identical monochromatic point sources in a single-slit diffraction pattern is 0.0065 rad. If a slit width of 0.10 mm is used, what is the wavelength of the sources?
What is the resolution limit due to diffraction for the European Southern Observatory reflecting telescope-50* (which has an 8.20-m, or 323-in., diameter) for light with a wavelength of 550 nm?
What is the resolution limit due to diffraction for the Hale telescope at Mount Palomar, with its 200-in.-diameter mirror, for light with a wavelength of 550 nm? Compare this value with the resolution limit for the European Southern Observatory telescope found in Exercise 48.
A nearsighted person has an uncorrected far point of 200 cm. Which type of contact lenses would correct this condition, and of what focal length should it be?
From a spacecraft in orbit 150 km above the Earth’s surface, an astronaut wishes to observe her hometown as she passes over it. What size features will she be able to identify with the unaided eye, neglecting atmospheric effects?
A human eye views small objects of different colors, and the eye's resolution is measured. (a) The eye sees the finest details for objects of which color: (1) red, (2) yellow, (3) blue, or (4) any color? Explain. (b) The maxi-mum diameter of the eye's pupil at night is about 7.0 mm. What are the
Some African tribes people claim to be able to see the moons of Jupiter with the unaided eye. If two moons of Jupiter are at a minimum distance of 3.1 X 108 km away from Earth and at a maximum separation distance of 3.0 X 106 km, is this possible in theory? Explain. Assume that the moons reflect
Assuming that the headlights of a car are point sources 1.7 m apart, what is the maximum distance from an observer to the car at which the headlights are distinguishable from each other?
If a camera with a 50-mm lens is to resolve two objects that are 4.0 mm from each other and both objects are 3.5 m from the camera lens, (a) What is the minimum diameter of the camera lens? (b) What is the resolving power? (Assume the wavelength of light is 550 nm.)
The objective of a microscope is 2.50 cm in diameter and has a focal length of 0.80 mm. (a) If blue light with a wavelength of 450 nm is used to illuminate a specimen, what is the minimum angular separation of two fine details of the specimen for them to be just resolved? (b) What is the
A refracting telescope with a lens whose diameter is 30.0 cm is used to view a binary star system that emits light in the visible region. (a) What is the minimum angular separation of the two stars for them to be barely resolved? (b) If the binary star is a distance of 6.00 x 1020 km from the
A radio telescope with a diameter of 300 m uses a wavelength of 4.0 m to observe a binary star system that is about 2.5 x 1018 km from the Earth. What is the mini-mum distance of two stars that can be distinguished by the telescope?
A microscope with an objective 1.20 cm in diameter is used to view a specimen via light from a mercury source with a wavelength of 546.1 nm.
A student uses a magnifying glass to examine the details of a microcircuit in the lab. If the lens has a power of 10 D and a virtual image is formed at the student’s near point (25 cm), (a) How far from the circuit is the lens held, and (b) What is the angular magnification?
A person can just see the print in a book clearly when she holds the book no closer than at arm’s length (0.45 m from the eyes). (a) Does she have (1) nearsightedness, (2) farsightedness, or (3) astigmatism? Explain. (b) Which type of lens will allow her to read the text at the normal near
Referring to Fig. 25.24, show that the magnifying power of a magnifying glass held at a distance d from the eye is given bywhen the actual object is located at the near point (25 cm).
Referring to Fig. 25.25, show that the angular magnification of a refracting telescope focused for the final image at infinity is m = €“ fo/fe. (Because telescopes are designed for viewing distant objects, the angular size of an object viewed with the unaided eye is the angular size of
A person with nearsightedness was prescribed with con-tact lenses of power – 2.0 D. By mistake, he was given lenses of power + 2.0 D. What is the range of object distances that this person can see clearly with the wrong lenses?
Two astronomical telescopes have the characteristics shown in the following table:
A refracting telescope has an objective with a focal length of 50 cm and an eyepiece with a focal length of 2.0 cm. The telescope is used to view an object that is 10 cm high and located 50 m away. What is the apparent angular height, in degrees, of the object as viewed through the telescope?
The amount of light that reaches the film in a camera depends on the lens aperture (the effective area) as con-trolled by the diaphragm. The f-number is the ratio of the focal length of the lens to its effective diameter. For example, an f/8 setting means that the diameter of the aperture is
To correct a case of farsightedness, an optometrist prescribes converging contact lenses that effectively move the patient’s near point from 85 cm to 25 cm. (a) What is the power of the lenses? (b) To see distant objects clearly, should the patient wear the contact lenses or take them out?
A woman cannot see objects clearly when they are farther than 12.5 m away. (a) Does she have (1) near-sightedness, (2) farsightedness, or (3) astigmatism? Explain. (b) Which type of lens will allow her to see distant objects clearly, and of what power should the lens be?
A man is unable to focus on objects nearer than 1.5 m. (a) Does he have (1) nearsightedness, (2) farsightedness, or (3) astigmatism? Explain. (b) The type of contact lenses that allows him to focus on the print of a book held 25 cm from his eyes should be (1) converging, (2) diverging, (3) flat.

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