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physics
light and optics
Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions
A beam of light in air strikes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.
Prove in general that for a light beam incident on a uniform layer of transparent material, as in Fig. 23-22, the direction of the direction of the emerging beam is parallel to the incident beam, independent of the incident angle θ. Assume air on both sides of the glass.
A light ray is incident on a flat piece of glass with index of refraction n as in Fig. 23-22. Show that if the incident angle θ is small, the emerging ray is displaced a distance d = t θ (n – 1) / n from the incident ray, where t is the thickness of the glass and θ is in radians.
What is the critical angle for the interface between water and Lucite? To be totally internally reflected, the light must start in which material??
A beam of light is emitted in a pool of water from a depth of 62.0cm. Where must it strike that air-water interface, relative to the spot directly above it, in order that the light does not exit the water? Explain.
A beam of light is emitted in a pool of water from a depth of 62.0cm. Where must it strike that air-water interface, relative to the spot directly above it, in order that the light does not exit the water?
A beam of light is emitted 8.0 cm beneath the surface of a liquid and strikes the surface 7.0cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid?
Suppose a ray strikes the left face of the prism in Fig. 23-51 at 45.0o as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is Ф = 75.0o, what can you say about the index of refraction of the prism?
A beam of light enters the end of an optic fiber as shown in Fig. 23-52. Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle a, the light beam reflects
(a) What is the minimum index of refraction for a glass or plastic prism to be used in binoculars (Fig. 23-26) so that total internal reflection occurs at 45o?(b) Will binoculars work if its prisms (assume n = 1.50) are immersed in water?(c) What minimum n is needed if the prisms are immersed in
A sharp image is located 78.0 mm behind a 65.0-mm-focal-length converging lens. Find the object distance(a) Using a ray diagram.(b) By calculation.
Sunlight is observed to focus at a point 18.5cm behind a lens.(a) What kind of lens is it?(b) What is its power in diopters?
A certain lens focuses light from an object 2.75m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?
(a) What is the power of a 20.5-cm-focal-length lens?(b) What is the focal length of a –6.25-diopter lens?(c) Are these lenses converging or diverging?
A stamp collector uses a converging lens with focal length 24cm to view a stamp 18cm in front of the lens.(a) Where is the image located?(b) What is the magnification?
A –5.5-D lens is held 14.0cm from and object 4.0mm high. What are the position, type, and height of the image?
An 80-mm-focal-length lens is used to focus an image on the film of a camera. The maximum distance allowed between the lens and the film plane is 120 mm. (a) How far ahead of the film should the lens be if the object to be photographed is 10.0m away? (b) 3.0 m away?(c) 1.0m away?(d) What is the
It is desired to magnify reading material by a factor of 2.5 x when a book is placed 8.0cm behind a lens. (a) Draw a ray diagram and describe the type of image this would be. (b) What type of lens is needed?(c) What is the power of the lens are diopters?
An object is located 1.5m from an 8.0-D lens. By how much does the image move if the object is moved(a) 1.0m closer to the lens, and(b) 1.0m farther from the lens?
How far from a converging lens with a focal length of 25cm should an object be placed to produce a real image which is the same size as the object?
(a) How far from a 50.0-mm-focal-length lens must an object be placed if its image is to be magnified 2.00 x and be real?(b) What if the image is to be virtual and magnified 2.00x?
Repeat Problem 53 for a –50.0mm-focal-length lens.
(a) A 2.00-cm-high insect is 1.20m from a 135-mm-focal-length lens. Where is the image, how high is it, and what type is it?(b) What if f = – 135mm?
How far apart are an object and an image formed by a 75-cm-focal-length converging lens if the image is 2.5 x larger than the object and is real?
A bright object and a viewing screen are separated by a distance of 66.0cm. At what location(s) between the object and the screen should a lens of focal length 12.5cm be placed in order to produce a crisp image on the screen?
Two 28.0-cm-focal-length converging lenses are placed 16.5cm apart. An object is placed 36.0cm in front of one lens. Where will the final image formed by the second lens be located? What is the total magnification?
A diverging lens with f = – 31.5cm is placed 14.0cm behind a converging lens with f = 20.0cm. Where will an object at infinity be focused?
A 31.0-cm-focal-length converging lens is 21.0cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens?
The two converging lenses of Example 23-12 are now placed only 20.0cm apart. The object is still 60.0cm in front of the first lens as in Fig. 23-41. In this case, determine(a) The position of the final image, and (b) The overall magnification.(c) Sketch the ray diagram for this system.
Two converging lenses are placed 30.0cm apart. The focal length of the lens on the right is 20.0cm, and the focal length of the lens on the left is 15.0cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the
A diverging lens with a focal length of –14 cm is placed 12cm to the right of a converging lens with a focal length of 18cm. An object is placed 33cm to the left of the converging lens.(a) Where will the final image be located?(b) Where will the image be if the diverging lens is 38cm from the
Two lenses, one converging with focal length 20.0cm and one diverging with focal length –10.0cm, are placed 25.0cm apart. An object is placed 60.0cm in front of the converging lens. Determine?(a) The position and (b) The magnification of the final image formed. (c) Sketch a ray diagram for this
A diverging lens is placed next to a converging lens of focal length fC, as in Fig. 23-42. If fT represents the focal length of the combination, show that the focal length of the diverging lens fD, is given by
A double concave lens has surface radii of 34.2 cm and 23.8cm. What is the focal length if n = 1.52?
Both surfaces of a double convex lens have radii of 31.0cm. If the focal length is 28.9cm, what is the index of refraction of the lens material?
A Plano concave lens (n = 1.50) has a focal length of –23.4cm. What is the radius of the concave surface?
A Lucite plano concave lens (see Fig. 23-29b) has one flat surface and the other has R = – 18.4cm. What is the focal length?
A symmetric double convex lens with a focal length of 25.0cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surface?
A prescription for a corrective lens calls for + 1.50 D the lens maker grinds the lens from a “blank” with n = 1.56 and a preformed convex front surface of radius of curvature of 40.0cm. What should be the radius of curvature of the other surface?
Two plane mirrors face each other 2.0m apart as in Fig. 23-53. You stand 1.5m away from one of these mirrors and look into it. You will see multiple images of yourself.(a) How far away from you are the first three images in the mirror in front of you?(b) Are these first three images facing toward
The critical angle of a certain piece of plastic in air is θC = 37.3o. What is the critical angle of the same plastic if it is immersed in water?
(a) A plane mirror can be considered a limiting case of a spherical mirror. Specify what this limit is.(b) Determine an equation that relates the image and object distances in this limit of a plane mirror. (c) Determine the magnification of a plane mirror in this same limit.(d) Are you results in
Stand up two plane mirrors so they form a 90o angle as in Fig. 23-55. When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs,
Show analytically that a diverging lens can never form a real image of a real object. Can you describe a situation in which a diverging lens can form a real image?
Each student in a physics lab is assigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical
If the apex angle of a prism is θ = 72o (see Fig. 23-56), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given n = 1.50?
The end faces of a cylindrical glass rod (n = 1.54) are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?
A lighted candle is placed 33cm in front of a converging lens of focal length f1 = 15cm, which in turn is 55cm in front of another converging lens of focal length f2 = 12cm (see Fig./ 23-57).(a) Draw a ray diagram and estimate the location and the relative size of the final image.(b) Calculate the
A bright object is placed on one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distance dT = di + do between the object and the screen is kept fixed, but the lens can be moved. (a) Show that if dT> 4f, there will be two positions
In a side or movie projector, the film acts as the object whose image is projected on a screen (Fig. 23-58). If a 105-mm-focal-length lens is to project an image on a screen 8.00m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen?
A 35-mm slide (picture size is actually 24 by 36 mm) is to be projected on a screen 1.80m by 2.70m placed 7.50m from the projector. What focal-length lens should be used if the image is to cover the screen?
Show analytically that the image formed by a converging lens is real and inverted if the object is beyond the focal point (do > f>, and is virtual and upright if the object is within the focal point (do < f>. Describe the image if the object is itself and image, formed by another lens, so its
A movie star catches a reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210mm. How far away from the subject
How large is the image of the Sun on film used in camera with?(a) A 28-mm-focal-length lens.(b) A 50-mm-focal-length lens, and (c) A 135-mm-focal-length lens?(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The sun
(a) An object 34.5 cm in front of a certain lens is imaged 8.20cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real or virtual?(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens
When an object is placed 60.0cm from a certain converging lens, it forms a real image. When the object is moved to 40.0cm from the lens, the image moves 10.0cm farther from the lens. Find the focal length of this lens.
A small object is 25.0cm from a diverging lens as shown in Fig. 23-59. A converging lens with a focal length of 12.0cm is 30.0cm to the right of the diverging lens. The two-lens system forms a real inverted image 17.0cm to the right of the converging lens. What is the focal length of the diverging
An object is placed 15cm from a certain mirror. The image is half the size of the object, inverted, and real. How far is the image from the mirror and what is the radius of curvature of the mirror?
(a) Show that the lens equation can be written in the Newtonian form xx` = f2, where x is the distance of the object from the focal point on the front side of the lens, and x` is the distance of the image to the focal point on the other side of the lens. Calculate the location of an image if the
A Converging lens with focal length of 10.0cm is placed in contact with a diverging lens with a focal length of –20.0cm. What is the focal length of the combination, and is the combination converging or diverging?
(a) Show that if two thin lenses of focal lengths f1 and f2 are placed in contact with each other, the focal length of the combination is given by fT = f1 f2 / (f1 + f2).(b) Show that the power P of the combination of two lenses is the sum of their separate powers, P = P1 + P2.
Does Huygens’ Principle apply to sound waves? To water waves? Explain.
What is the evidence that light is energy?
Why is light sometimes described as rays and sometimes as waves?
We can hear sounds around corners, but we cannot see around comers; yet both sound and light are waves. Explain the difference.
If Young’s double-slit experiment were submerged in water, how would the fringe pattern be changed?
Monochromatic red light is incident on a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the red light source is replaced by a blue light source.
For diffraction by a single slit, what is the effect of increasing? (a) The slit width, and (b) The wavelength?
Why was the observation of the double-slit interference pattern more convincing evidence for the wave theory of light than the observation of diffraction?
Compare a double-slit experiment for sound waves to that for light waves. Discuss the similarities and differences.
Why doesn’t the light from the two headlights of a distant car produce and interference pattern?
Suppose white light falls on the two slits of Fig. 24-7, but one slit is covered by a red filter (700nm) and the other by a blue filter (450nm). Describe the pattern on the screen.
When white light passes through a flat piece of window glass, it is not broken down into colors as it is by a prism. Explain.
For both converging and diverging lenses, discuss how the focal length for red light differs from that for violet light.
A ray of light is refracted through three different materials (Fig. 24-55). Rank the materials according to their index of refraction, least to greatest.
Hold one hand close to your eye and focus on a distant light source through a narrow slit between two fingers. (Adjust your fingers to obtain the best pattern). Describe the pattern that you see.
What happens to the diffraction pattern of a single slit if the whole apparatus is immersed in? (a) Water,(b) A Vacuum, instead of in air.
For diffraction by a single slit, what is the effect of increasing? (a) The slit width, and (b) The wavelength? Discuss.
What is the difference in the interference patterns formed?(a) By two slits 10-4 cm apart,(b) By a diffraction grating containing 104 lines/cm?
For a diffraction grating, what is the advantage of?(a) Many slits, (b) Closely spaced slits?
White light strikes?(a) A diffraction grating, and (b) A Prism, A rainbow appears on a wall just below the direction of the horizontal incident beam in each case. What is the color of the top of the rainbow in each case? Explain.
For light consisting of wavelengths between 400nm and 700nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?
Why are interference fringes noticeable only for a thin film like a soap bubble and not for a thick piece of glass, say?
When a compact dist (CD) is held at an angle in white light, the reflected light is a full spectrum (Fig. 24-56). Explain. What would you expect to see if monochromatic light was used?
Why are Newton’s rings (Fig. 24-31) closer together farther from the center?
Some coated lenses appear greenish yellow when seen by reflected light. What wavelengths do you suppose the coating is designed to transmit completely?
A drop of oil on a pond appears bright at its edges, where its thickness is much less than the wavelengths of visible light. What can you say about the index of refraction of the oil?
What does polarization tell us about the nature of light?
Explain the advantage of polarized sunglasses over normal tinted sunglasses.
How can you tell if a pair of sunglasses is polarizing or not?
Two polarized sheets rotated at an angle of 90o with respect to each other will not let any light through. Three polarized sheets, each rotated at an angle of 45o with respect to each other, will let some light through. What will happen to unpolarized light if you align four polarized sheets each
What would be the color of the sky if the Earth had no atmosphere?
If the Earth’s atmosphere were 50 times denser than it is would sunlight still be white, or would it be some other color?
Monochromatic light falling on two slits 0.016mm apart produces the fifth-order fringe at an 8.8o angle. What is the wavelength of the light used?
The third-order fringe of 610nm light is observed at an angle of 18o when the light falls on two narrow slits. How far apart are the slits?
Monochromatic light falls on two very narrow slits 0.048mm apart. Successive fringes on a screen 5.00m away are 6.5cm apart near the center of the pattern. Determine the wavelength and frequency of the light.
A parallel beam of light from a He-Ne laser, with a wavelength 656nm, falls on two very narrow slits 0.060mm apart. How far apart are the fringes in the center of the pattern on a screen 3.6m away?
Light of wavelength 680nm falls on two slits and produces an interference pattern in which the fourth-order fringe is 38mm from the central fringe on a screen 2.0m away. What is the separation of the two slits?
If 720-nm and 660-nm light passes through two slits 0.58mm apart, how far apart are the second-order fringes for these two wavelengths on a screen 1.0m away?
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