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physics
light and optics

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

An object 4.0 cm tall is in front of a converging lens of focal length 22 cm. The object is 15 cm away from the lens. (a) Use a ray diagram to determine whether the image is (1) real or virtual, (2) upright or inverted, and (3) magnified or reduced. (b) Calculate the image distance and lateral
(a) Design the lens in a single-lens slide projector that will form a sharp image on a screen 4.0 m away with the transparent slides 6.0 cm from the lens. (b) If the object on a slide is 1.0 cm tall, how tall will the image on the screen be?
An object is placed in front of a concave lens whose focal length is – 18cm. Where is the image located and what are its characteristics, if the object distance is (a) 10 cm and (b) 25 cm? Sketch ray diagrams for each case.
A convex lens produces a real, inverted image of an object that is magnified 2.5 times when the object is 20 cm from the lens. What are the image distance and the focal length of the lens?
A convex lens has a focal length of 0.12 m. Where on the lens axis should an object be placed in order to get (a) A real, magnified image with a magnification of 2.0 and (b) A virtual, magnified image with a magnification of 2.0?
A small dog sits 3.0 m in front of a plane mirror. (a) Where is the dog’s image in relation to the mirror? (b) If the dog jumps at the mirror at a speed of 1.0 m/s, how fast does the dog approach its image?
Using the thin lens equation and the magnification factor, show that for a spherical diverging lens, the image of a real object is always virtual, upright, and reduced.
A simple single-lens camera (convex lens) is used to photograph a man 1.7 m tall who is standing 4.0 m from the camera. If the man’s image fills the height of a frame of film (35 mm), what is the focal length of the lens?
To photograph a full moon, a photographer uses a single-lens camera with a focal length of 60 mm. What will be the diameter of the Moon’s image on the film?
An object 5.0 cm tall is 10 cm from a concave lens. The resulting virtual image is one-fifth as large as the object. What is the focal length of the lens and the image distance?
An object is placed 80 cm from a screen. (a) At what point from the object should a converging lens with a focal length of 20 cm be placed so that it will produce a sharp image on the screen? (b) What is the image’s magnification?
(a) For a convex lens, what is the minimum distance between an object and its image if the image is real? (b) What is the minimum distance if the image is virtual?
Using Fig. 23.28, derive(a) The thin lens equation and (b) The magnification equation for a thin lens.
(a) If a book is held 30 cm from an eyeglass lens with a focal length of – 45 cm, where is the image of the print formed? (b) If an eyeglass lens with a focal length of + 57 cm is used, where is the image formed?
To correct myopia (nearsightedness), concave lenses are prescribed. If a student can read her physics book only when she holds it no farther than 18 cm away, what focal length of lens should be prescribed so she can read when she holds the book 35 cm away?
A woman fixing the hair on the back of her head holds a plane mirror 30 cm in front of her face so as to look into a plane mirror on the bathroom wall behind her. She is 90 cm from the wall mirror. (a) The image of the back of her head will be from (1) only the front mirror, (2) only the wall
To correct hyperopia (farsightedness), convex lenses are prescribed. If a senior citizen can read a newspaper only when he holds it no closer than 50 cm away, what focal length of lens should be prescribed so he can read when he holds the newspaper 25 cm away?
A biology student wants to examine a bug at a magnification of + 5.00 (a) The lens should be (1) convex, (2) concave, (3) flat. Explain. (b) If the bug is 5.00 cm from the lens, what is the focal length of the lens?
The human eye is a complex multiple-lens system. However, it can be approximated to an equivalent single converging lens with an average focal length about 1.7 cm when the eye is relaxed. If an eye is viewing a 2.0-m-tall tree located 15 m in front of the eye, what are the height and orientation of
The geometry of a compound microscope, which consists of two converging lenses, is shown in Fig. 23.29. (More detail on microscopes is given in Chapter 25.) The objective lens and the eyepiece lens have focal lengths of 2.8 mm and 3.3 cm, respectively. If an object is located 3.0 mm from the
Two converging lenses L1 and L2 have focal lengths of 30 cm and 20 cm, respectively. The lenses are placed 60 cm apart along the same axis, and an object is placed 50 cm from L1 (110 cm from L2). Where is the image formed relative to L2, and what are its characteristics?
For a lens combination, show that the total magnification Mtotal = M1 M2.
Show that for thin lenses that have focal lengths f1 and f2 and are in contact, the effective focal length (f) is given by
An optometrist prescribes glasses with a power of – 4.0 D for a nearsighted student. What is the focal length of the glass lenses?
A plastic convex meniscus (Fig. 23.14) contact lens is made of plastic with an index of refraction of 1.55. The lens has a front radius of 2.50 cm and a back radius of 3.00 cm. (a) The signs of R1 and R2 are (1) +, +, (2) +, -, (3) -, +, (4) -, -. Explain. (b) What is the focal length of the lens?
(a) When you stand between two plane mirrors on opposite walls in a dance studio, you observe (1) one, (2) two, or (3) multiple images. Explain. (b) If you stand 3.0 m from the mirror on the north wall and 5.0 m from the mirror on the south wall, what are the image distances for the first two
A plastic plano-concave lens has a radius of curvature of 50 cm for its concave surface. If the index of refraction of the plastic is 1.35, what is the power of the lens?
An optometrist prescribes a corrective lens with a power of +1.5 D. The lens maker starts with a glass blank that has an index of refraction of 1.6 and a convex front surface whose radius of curvature is 20 cm. To what radius of curvature should the other surface be ground? Is the surface convex or
A converging glass lens with an index of refraction of 1.62 has a focal length of 30 cm in air. (a) When the lens is immersed in water, the focal length of the lens will (1) increase, (2) remain the same, (3) decrease. Explain. (b) What is the focal length when the lens is submerged in water?
A biconvex lens is made of glass whose index of refraction is 1.6. The lens has a radius of curvature of 30 cm for one surface and 40 cm for the other. Calculate the focal length of this lens as used in air and under water.
A lens made of fused quartz (n = 1.46) has a focal length of +45 when it is in air. (a) If the lens is immersed in oil (n = 1.50), the lens will (1) remain con-verging, (2) become diverging, (3) have an infinite focal length. Explain. (b) What is the focal length when it is in oil?
(a) Use ray diagrams to show that a ray parallel to the optic axis of a biconvex lens is refracted toward the axis at the incident surface and again at the exit surface. (b) Show that this also holds for a biconcave lens, but with both refractions pointing away from the axis.
An object is 40 cm from a converging lens whose focal length is 20 cm. On the opposite side of that lens, at a distance of 60 cm, is a plane mirror. Where is the final image measured from the lens, and what are its characteristics?
A method of determining the focal length of a diverging lens is called auto collimation. As Fig. 23.30 shows, first a sharp image of a light source is projected onto a screen by a converging lens. Second, the screen is replaced with a plane mirror. Third, a diverging lens is placed between the
For the arrangement shown in Fig. 23.31, an object is placed 0.40 m in front of the converging lens, which has a focal length of 0.15 m. If the concave mirror has a focal length of 0.13 m, where is the final image formed, and what are its characteristics?
A student is given a piece of glass (n = 1.60) to make a symmetrical biconvex lens so it can form an image with a magnification of when the object is 5.00 m from the lens. What should be the radius of curvature of the lens surfaces?
A woman 1.7 m tall stands 3.0 m in front of a plane mirror. (a) What is the minimum height the mirror must be to allow the woman to view her complete image from head to foot? Assume that her eyes are 10 cm below the top of her head. (b) What would be the required mini-mum height of the mirror if
Two lenses, each having a power of + 10 D, are placed 20 cm apart along the same axis. If an object is 60 cm from the first lens (not in between the lenses), where is the final image relative to the first lens, and what are its characteristics?
Certain people wear bifocal glasses to improve their near and far vision. If a person can only see things clearly from a distance of 40.0 cm to 80.0 cm from his eyes without glasses, what powers of bifocal glasses should she wear so she can see things clearly from 25.0 cm to infinity?
Prove that do = |di| (equal magnitude) for a plane mirror.
Given two pairs of sunglasses, could you tell whether one or both were polarizing?
Suppose that you held two polarizing sheets in front of you and looked through both of them. How many times would you see the sheets lighten and darken (a) If one were rotated through one complete rotation, (b) If both were rotated through one complete rotation at the same speed in opposite
Explain why the sky may be red in the morning and evening and blue during the day.
To study wave interference, a student uses two speakers driven by the same sound wave of wavelength 0.50 m. If the distances from a point to the speakers differ by 0.75 m, will the waves interfere constructively or destructively at that point? What if the distances differ by 1.0 m?
Two parallel slits are illuminated with monochromatic light, and an interference pattern is observed on a screen. (a) If the distance between the slits were decreased, would the distance between the maxima (1) increase, (2) remain the same, or (3) decrease? Explain. (b) If the slit separation is
(a) In a double-slit experiment, if the distance from the double slits to the screen is increased, the separation between the adiacent maxima will (1) increase, (2) decrease, (3) remain the same. Explain. (b) Yellow-green light (λ = 550 nm) illuminates a double-slit separated by 1.75 x 10-4 m. If
(a) Derive a relationship that gives the locations of the minima in a Young’s double-slit experiment. What is the distance between adjacent minima? (b) For a third-order minimum (the third side dark position from the central maximum), what is the path length difference between that location and
When a double-slit setup is illuminated with light of wavelength 632.8 nm, the distance between the center of the central bright position and the second side dark position is 4.5 cm on a screen that is 2.0 m from the slits. What is the distance between the slits?
(a) If the apparatus for a Young’s double-slit experiment were completely immersed in water, would the spacing of the interference maxima (1) increase, (2) remain the same, or (3) decrease? Explain. (b) What would the lateral displacements in Exercise 6 be if the entire system were immersed in
Light of two different wavelengths is used in a double-slit experiment. The location of the third-order maxi-mum for the first light, yellow-orange light (λ = 600 nm), coincides with the location of the fourth-order maximum for the other color’s light. What is the wavelength of the other light?
Light of wavelength 550 nm in air is normally incident on a glass plate (n = 1.5) whose thickness is 1.1 x 10-5 m. (a) What is the thickness of the glass expressed in terms of the wavelength of light in glass? (b) How many reflected waves will experience the phase shift? (c) Will the reflected
A film of index of refraction of 1.4 and thickness of 1.2 x 10-5m is on a lens with an index of refraction of 1.6. Light of wavelength 600 nm is incident normally from air to the film. Consider only reflections from the top and bottom surfaces of the film. (a) How many reflected waves will
A lens with an index of refraction of 1.60 is to be coated with a material (n = 1.40) that will make the lens nonreflecting for yellow-orange (λ = 515nm) light normally incident on the lens. What is the minimum required thickness of the coating?
Magnesium fluoride (n = 1.38) is frequently used as a lens coating to make nonreflecting lenses. What is the difference in the minimum film thickness required for maximum transmission of blue light (λ = 400 nm)and of red light (λ = 700 nm)?
In the development of Young’s double-slit experiment, a small-angle approximation (tan θ ≈ sin θ) was used to find the lateral displacements of the maxima (bright) and minima (dark) positions. How good is this approximation? For example, what is the percentage error for θ = 10o?
A film on a lens with an index of refraction of 1.5 is 1.0 x 10-7 m thick and is illuminated with white light. The index of refraction of the film is 1.4. (a) The number of waves that experience the phase shift is (1) zero, (2) one, (3) two. Explain. (b) For what wavelength of visible light will
A solar cell is designed to have a nonreflective film of a transparent material for a wavelength of 550 nm. (a) Will the thickness of the film depend on the index of refraction of the underlying material in the solar cell? Discuss the possible scenarios. (b) If nsolar > nfilm and nfilm – 1.22,
A thin layer of oil (n = 1.50) floats on water. Destructive interference is observed for reflected light of wavelengths 480 nm and 600 nm, each at a different location. (a) If the order number is the same for both wave-lengths, which wavelength is at a greater thickness: (1) 480 nm, or (2) 600 nm?
Two parallel plates are separated by a small distance as illustrated in Fig. 24.29. If the top plate is illuminated with light from a He€“ Ne laser (Î» = 632.8nm), for what minimum separation distances will the light be(a) Constructively reflected and (b) Destructively
An air wedge such as that shown in Fig. 24.30 can be used to measure small dimensions, such as the diameter of a thin wire.(a) If the top glass plate is illuminated with monochromatic light, the interference pattern observed will be (1) bright, (2) dark, (3) bright and dark lines based on the air
The glass plates in Fig. 24.30 are separated by a thin, round filament. When the top plate is illuminated normally with light of wavelength 550 nm, the filament lies directly below the sixth maximum (bright) position. What is the diameter of the filament?
A slit of width 0.15 mm is illuminated with monochromatic light of wavelength 632.8 nm. At what angle will the first minimum occur?
In a single-slit diffraction pattern using light of wave-length 550 nm, the second-order minimum is measured to be at 0.32°. What is the slit width?
A slit of width 0.20 mm is illuminated with monochromatic light of wavelength 480 nm, and a diffraction pattern is formed on a screen 1.0 m from the slit. (a) What is the width of the central maximum? (b) What are the widths of the second-and third-order maxima?
A slit 0.025 mm wide is illuminated with red light (λ = 680 nm). How wide are (a) The central maximum and (b) The side maxima of the diffraction pattern formed on a screen 1.0 m from the slit?
Two parallel slits 0.075 mm apart are illuminated with monochromatic light of wavelength 480 nm. Find the angle between the center of the central maximum and the center of the first side maximum.
At what angle will the second-order maximum be seen from a diffraction grating of spacing 1.25 μm when illuminated by light of wavelength 550 nm?
A venetian blind is essentially a diffraction grating—not for visible light, but for waves with much longer wave-lengths. If the spacing between the slats of a blind is 2.5 cm, (a) For what wavelength would there be a first-order maximum at an angle of 10o, and (b) What type of radiation is
A single slit is illuminated with monochromatic light, and a screen is placed behind the slit to observe the diffraction pattern. (a) If the width of the slit is increased, will the width of the central maximum (1) increase, (2) remain the same, or (3) decrease? Why? (b) If the width of the slit
(a) If the wavelength used in a single-slit diffraction experiment increases, will the width of the central maximum (1) increase, (2) remain the same, or (3) decrease? Why? (b) If the width of the slit is 0.45 mm, the wavelength is 400 nm, and the screen is 2.0 m from the slit, what would be the
A teacher standing in a doorway 1.0 m wide blows a whistle with a frequency of 1000 Hz to summon children from the playground (Fig. 24.31). Two boys are playing on the swings 20 m away from the school building. One boy is at an angle of Î¸o and another one 19.6o at from a line normal to
A diffraction grating is designed to have the second-order maxima at 10o from the central maximum for red light (λ = 700 nm). How many lines per centimeter does the grating have?
Find the angles of the blue (λ = 420nm) and red components of the first-and second-order maxima in a pattern produced by a diffraction grating with 7500 lines/cm.
A certain crystal gives a deflection angle of 25o for the first-order maximum of monochromatic X-rays with a frequency of 5.0 x 1017 Hz. What is the lattice spacing of the crystal?
(a) Only a limited number of maxima can be observed with a diffraction grating. The factor(s) that limit(s) the number of maxima seen is (are) (a) (1) the wave-length, (2) the grating spacing, (3) both. Explain. (b) How many maxima appear when monochromatic light of wave-length 560 nm illuminates
A diffraction grating with is illuminated with a red light from a He– Ne laser (λ = 632.8 nm). How many side maxima are formed in the diffraction pattern, and at what angles are they observed?
When two parallel slits are illuminated with mono-chromatic light of wavelength 632.8 nm, the angle between the center of the central maximum and the center of the second side maximum is 0.45o. What is the distance between the parallel slits?
In a particular diffraction grating pattern, the red component (700 nm) in the second-order maximum is deviated at an angle of 20o. (a) How many lines per centimeter does the grating have? (b) If the grating is illuminated with white light, how many maxima of the complete visible spectrum would
The commonly used CD (Compact Disc) consists of many closely spaced tracks that can be used as reflecting gratings. The industry standard for the track-to-track distance is 1.6μm. If a He–Ne laser with a wavelength of 632.8 nm is incident normally onto a CD, calculate the angles for all the
White light of wavelength ranging from 400 nm to 700 nm is used for a diffraction grating with 6500 lines per centimeter. (a) In a particular order of maximum, red color will have (1) a larger, (2) the same, or (3) a smaller angle than blue color. Explain. (b) Calculate the angles for 400 nm and
White light ranging from blue (400 nm) to red (700 nm) illuminates a diffraction grating with 8000 lines/cm. (a) For the first maxima measured from the central maximum, the blue color is (1) closer to, (2) farther from, or (3) at the same location as the red color. Explain. (b) What are the
White light whose components have wavelengths from 400 nm to 700 nm illuminates a diffraction grating with 4000 lines/cm. Do the first-and second-order spectra overlap? Justify your answer.
Show that for a diffraction grating, the violet (λ = 400 nm) portion of the third-order maximum over-laps the yellow-orange (λ = 600 nm) portion of the second-order maximum, regardless of the grating’s spacing.
Un polarized light is incident on a polarizer–analyzer pair that can have their transmission axes at an angle of either 30o or 45o. (a) The angle will allow (1) more, (2) the same, or (3) less light to go through. (b) Calculate the percentage of light that goes through the polarizer– analyzer
When un polarized light is incident on a polarizer–analyzer pair, 30% of the original light intensity passes the analyzer. What is the angle between the transmission axes of the polarizer and analyzer?
Some types of glass have a range of indices of refraction of about 1.4 to 1.7. What is the range of the polarizing (Brewster) angle for these glasses when light is incident on them from air?
Light is incident on a certain material in air. (a) If the index of refraction of the material increases, the polarizing (Brewster) angle will (1) also increase, (2) decrease, (3) remain the same. Explain. (b) What are the polarizing angles if the index of refraction is 1.6 and 1.8?
In a double-slit experiment that uses monochromatic light, the angular separation between the central maxi-mum and the second-order maximum is 0.16o. What is the wavelength of the light if the distance between the slits is 0.350 mm?
Un polarized light of intensity Io is incident on a polarizer– analyzer pair. (a) If the angle between the polarizer and analyzer increases in the range of to , the transmitted light intensity will (1) also increase, (2) decrease, (3) remain the same. Explain. (b) If the angle between the
A beam of light is incident on a glass plate in air and the reflected ray is completely polarized. What is the angle of refraction for the beam?
The critical angle for total internal reflection in a certain media boundary is 45o. What is the polarizing (Brewster) angle for light externally incident on the same boundary?
The polarizing (Brewster) angle for a certain media boundary is 33°. What is the critical angle for total internal reflection for the same boundary?
The angle of incidence is adjusted so there is maximum linear polarization for the reflected light from a transparent piece of plastic in air. (a) There is (1) no, (2) maximum, or (3) some light transmitted through the plastic. Explain. (b) If the index of refraction of the plastic is 1.40, what
(a) The polarizing (Brewster) angle of a piece of flint glass (n = 1.66) in water is (1) greater than, (2) less than, (3) the same as that of the glass in air. Explain. (b) What are the polarizing angles when it is in air and submerged in water, respectively?
Sunlight is reflected off a vertical plate-glass window (n = 1.55). What would the Sun’s altitude (angle above the horizon) have to be for the reflected light to be completely polarized?
A plate of crown glass (n = 1.52) is covered with a layer of water. A beam of light traveling in air is incident on the water and partially transmitted. Is there any angle of incidence for which the light reflected from the water–glass interface will have maximum linear polarization? Justify your
Sunlight is scattered by air molecules. (a) The intensity of the scattered blue light is (1) greater, (2) the same as, or (3) less than that of the scattered red light. Explain. (b) Calculate the ratio of the scattered light intensity of blue color (400 nm) to that of red color (700 nm).
When sunlight is scattered by air molecules, the intensity of scattered light for a wavelength of 550 nm is greater than another color by a factor of 5.0. (a) The wavelength of the other color is (1) longer, (2) the same as, or (3) shorter than 550 nm. Explain. (b) What is the wavelength of the
Monochromatic light passes through two narrow slits and forms an interference pattern on a screen. (a) If the wavelength of light used increases, will the distance between the maxima (1) increase, (2) remain the same, or (3) decrease? Explain. (b) If the slit separation is 0.25 mm, the screen is
A thin air wedge between two flat glass plates forms bright and dark interference bands when illuminated with normally incident monochromatic light. (a) Show that the thickness of the air wedge changes by λ/2 from one bright band to the next, where λ is the wavelength of the light. (b) What

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