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physics
light and optics
Fundamentals of Ethics for Scientists and Engineers 1st Edition Edmund G. Seebauer, Robert L. Barry - Solutions
A certain telescope uses a concave spherical mirror of radius 8 m. Find the location and diameter of the image of the moon formed by this mirror. The moon has a diameter of 3.5 × 106 m and is 3.8 × 108 m from the earth.
A concave spherical mirror has a radius of curvature of 6.0 cm. A point object is on the axis 9 cm from the mirror. Construct a precise ray diagram showing rays from the object that make angles of 5°, 10°, 30°, and 60° with the axis, strike the mirror, and are reflected back across the axis.
A concave mirror has a radius of curvature 6.0 cm. Draw rays parallel to the axis at 0.5, 1.0, 2.0, and 4.0 cm above the axis and find the points at which the reflected rays cross the axis. (Use a compass to draw the mirror and a protractor to find the angle of reflection for each ray.)(a) What is
An object placed 8 cm from a concave spherical mirror produces a virtual image 10 cm behind the mirror.(a) If the object is moved back to 25 cm from the mirror, where is the image located?(b) Is it real or virtual?
An object located 100 cm from a concave mirror forms a real image 75 cm from the mirror. The mirror is then turned around so that its convex side faces the object. The mirror is moved so that the image is now 35 cm behind the mirror. How far was the mirror moved? Was it moved toward or away from
Parallel light from a distant object strikes the large mirror in Figure (r = 5 m) and is reflected by the small mirror that is 2 m from the large mirror. The small mirror is actually spherical, not planar as shown. The light is focused at the vertex of the large mirror.(a) What is the radius of
A woman uses a concave makeup mirror with a radius of curvature of 1.5 m. How far from the mirror should her face be for the image to be 80 cm from her face?
A sheet of paper with writing on it is protected by a thick glass plate having an index of refraction of 1.5. If the plate is 2 cm thick, at what distance beneath the top of the plate does the writing appear when it is viewed from directly overhead?
A fish is 10 cm from the front surface of a fish bowl of radius 20 cm.(a) Where does the fish appear to be to someone in air viewing it from in front of the bowl?(b) Where does the fish appear to be when it is 30 cm from the front surface of the bowl?
A very long glass rod of 2-cm diameter has one end ground to a convex spherical surface of radius 5 cm. Its index of refraction is 1.5.(a) A point object in air is on the axis of the rod 20 cm from the surface. Find the image and state whether it is real or virtual. Repeat for(b) An object 5 cm
At what distance from the rod of Problem 30 should the object be placed so that the light rays in the rod are parallel? Draw a ray diagram for this situation.
Repeat Problem 30 for a glass rod with a concave hemispherical surface of radius –5 cm.
Repeat Problem 30 when the glass rod and objects are immersed in water.
Repeat Problem 30 for a glass rod with a concave hemispherical surface of radius –5 cm when it and the objects are immersed in water.
A glass rod 96 cm long with an index of refraction of 1.6 has its ends ground to convex spherical surfaces of radii 8 cm and 16 cm. A point object is in air on the axis of the rod 20 cm from the end with the 8-cm radius.(a) Find the image distance due to refraction at the first surface.(b) Find the
Under what conditions will the focal length of a thin lens be positive? Negative?
The following thin lenses are made of glass with an index of refraction of 1.5. Make a sketch of each lens, and find its focal length in air:(a) Double convex, r1 = 10 cm and r2 = –21 cm;(b) Plano–convex, r1 = ∞ and r2 = –10 cm;(c) Double concave, r1 = –10 cm and r2 = +10 cm;(d)
Glass with an index of refraction of 1.6 is used to make a thin lens that has radii of equal magnitude. Find the radii of curvature and make a sketch of the lens if the focal length in air is(a) +5 cm and(b) –5 cm.
Find the focal length of a glass lens of index of refraction 1.62 that has a concave surface with radius of magnitude 100 cm and a convex surface with a radius of magnitude 40 cm.
A double-concave lens of index of refraction 1.45 has radii of magnitudes 30 cm and 25 cm. An object is located 80 cm to the left of the lens. Find,(a) The focal length of the lens,(b) The location of the image, and(c) The magnification of the image.(d) Is the image real or virtual? Upright or
The following thin lenses are made of glass of index of refraction 1.6. Make a sketch of each lens, and find its focal length in air:(a) r1 = 20 cm, r2 = 10 cm;(b) r1 = 10 cm, r2 = 20 cm;(c) r1 = –10 cm, r2 = –20 cm.
For the following object distances and focal lengths of thin lenses in air, find the image distance and the magnification and state whether the image is real or virtual and erect or inverted:(a) s = 40 cm, f = 20 cm;(b) s = 10 cm, f = 20 cm;(c) s = 40 cm, f = –30 cm;(d) s = 10 cm, f = –30 cm.
An object 3.0 cm high is placed 20 cm in front of a thin lens of power 20 D. Draw a precise ray diagram to find the position and size of the image and check your results using the thin-lens equation.
Repeat Problem 47 for an object 1.0 cm high placed 10 cm in front of a thin lens of power 20 D.
Repeat Problem 47 for an object 1.0 cm high placed 10 cm in front of a thin lens whose power is –20 D.
(a) What is meant by a negative object distance? How can it occur? Find the image distance and magnification and state whether the image is virtual or real and erect or inverted for a thin lens in air when(b) s = –20 cm, f = +20 cm and(c) s = –10 cm, f = –30 cm. Draw a ray diagram for each of
Two converging lenses, each of focal length 10 cm, are separated by 35 cm. An object is 20 cm to the left of the first lens.(a) Find the position of the final image using both a ray diagram and the thin-lens equation.(b) Is the image real or virtual? Erect or inverted?(c) What is the overall
Work Problem 51 for a second lens that is a diverging lens of focal length –15 cm.
A thin lens of index of refraction 1.5 has one convex side with a radius of magnitude 20 cm. When an object 1 cm in height is placed 50 cm from this le ns, an upright image 2.15 cm in height is formed.(a) Calculate the radius of the second side of the lens. Is it concave or convex?(b) Draw a sketch
(a) Show that to obtain a magnification of magnitude m with a converging thin lens of focal length f, the object distance must be given by s = (m – 1)f/m.(b) A camera lens with 50-mm focal length is used to take a picture of a person 1.75 m tall. How far from the camera should the person stand so
An object is 15 cm in front of a positive lens of focal length 15 cm. A second positive lens of focal length 15 cm is 20 cm from the first lens. Find the final image and draw a ray diagram.
Work Problem 55 for a second lens with a focal length of –15 cm.
In a convenient form of the thin-lens equation used by Newton, the object and image distances are measured from the focal points. Show that if x = s – f and x’ = s’ – f, the thin-lens equation can be written as xx’ = f2, and the lateral magnification is given by m = –x’/f = –f/x.
An object is placed 2.4 m from a screen, and a lens of focal length f is placed between the object and the screen so that a real image of the object is formed on the screen. When the lens is moved 1.2 m toward the screen, another real image of the object is formed on the screen.(a) Where was the
An object is 17.5 cm to the left of a lens of focal length 8.5 cm. A second lens of focal length –30 cm is 5 cm to the right of the first lens.(a) Find the distance between the object and the final image formed by the second lens.(b) What is the overall magnification?(c) Is the final image real
A double-convex lens of radii r1 = +10 cm and r2 = –10 cm is made from glass with indexes of refraction of 1.53 for blue light and 1.47 for red light. Find the focal length of this lens for(a) Red light and(b) Blue light.
Suppose the eye were designed like a camera with a lens of fixed focal length f = 2.5 cm that could move toward or away from the retina. Approximately how far would the lens have to move to focus the image of an object 25 cm from the eye onto the retina?
Find the change in the focal length of the eye when an object originally at 3 m is brought to 30 cm from the eye.
Find(a) The focal length and(b) The power of a lens that will produce an image at 80 cm from the eye of a book that is 30 cm from the eye.
A farsighted person requires lenses with a power of 1.75 D to read comfortably from a book that is 25 cm from the eye. What is that person’s near point without the lenses?
If two point objects close together are to be seen as two distinct objects, the images must fall on the retina on two different cones that are not adjacent. That is, there must be an unactivated cone between them. The separation of the cones is about 1 μm.(a) What is the smallest angle the two
A person with a near point of 80 cm needs to read from a computer screen that is 45 cm from her eye.(a) Find the focal length of the lenses in reading glasses that will produce an image of the screen at 80 cm from her eye.(b) What is the power of the lenses?
A nearsighted person cannot focus clearly on objects more distant than 225 cm from her eye. What power lenses are required for her to see distant objects clearly?
Since the index of refraction of the lens of the eye is not very different from that of the surrounding material, most of the refraction takes place at the cornea, where n changes abruptly from 1.0 in air to about 1.4. Assuming the cornea to be a homogeneous sphere with an index of refraction of
The near point of a certain person is 80 cm. Reading glasses are prescribed so that he can read a book at 25 cm from his eye. The glasses are 2 cm from the eye. What diopter lens should be used in the glasses?
At age 45, a person is fitted for reading glasses of power 2.1 D in order to read at 25 cm. By the time she reaches 55, she discovers herself holding her newspaper at a distance of 40 cm in order to see it clearly with her glasses on.(a) Where was her near point at age 45?(b) Where is her near
An aging physics professor discovers that he can see objects clearly only between 0.75 m and 2.5 m so he decides he needs bifocals. The upper part of the lens allows him to see objects clearly at infinity, and the lower part allows him to see objects clearly at 25 cm. Assume that the lens is 2 cm
A person with a near-point distance of 30 cm uses a simple magnifier of power 20 D. What is the magnification obtained if the final image is at infinity?
A person with a near point distance of 25 cm wishes to obtain a magnifying power of 5 with a simple magnifier. What should be the focal length of the lens used?
What is the magnifying power of a lens of focal length 7 cm when the image is viewed at infinity by a person whose near point is at 35 cm?
A lens of focal length 6 cm is used as a simple magnifier with the image at infinity by one person whose near point is 25 cm and by another whose near point is 40 cm. What is the effective magnifying power of the lens for each person? Compare the size of the image on the retina when each looks at
A botanist examines a leaf using a convex lens of power 12 D as a simple magnifier. What is the expected angular magnification if(a) The final image is at infinity, and(b) The final image is at 25 cm?
(a) Show that if the final image of a simple magnifier is to be at the near point of the eye rather than at infinity, the angular magnification is given by(b) Find the magnification of a 20-D lens for a person with a near point of 30 cm if the final image is at the near point. Draw a ray diagram
A microscope objective has a focal length of 0.5 cm. It forms an image at 16 cm from its second focal point. What is the magnifying power for a person whose near point is at 25 cm if the focal length of the eyepiece is 3 cm?
A microscope has an objective of focal length 16 mm and an eyepiece that gives an angular magnification of 5 for a person whose near point is 25 cm. The tube length is 18 cm.(a) What is the lateral magnification of the objective?(b) What is the magnifying power of the microscope?
A crude symmetric hand-held microscope consists of two converging 20-D lenses fastened in the ends of a tube 30 cm long.(a) What is the “tube length” of this microscope?(b) What is the lateral magnification of the objective?(c) What is the magnifying power of the microscope?(d) How far from the
A compound microscope has an object with a power of 45 D and an eyepiece with a power of 80 D. The lenses are separated by 28 cm. Assuming that the final image is formed 25 cm from the eye, what is the magnifying power?
A microscope has a magnifying power of 600, and an eyepiece of angular magnification of 15. The objective lens is 22 cm from the eyepiece. Without making any approximations, calculate(a) The focal length of the eyepiece,(b) The location of the object such that it is in focus for a normal relaxed
A simple telescope has an objective with a focal length of 100 cm and an eyepiece of focal length 5 cm. It is used to look at the moon, which subtends an angle of about 0.009 rad.(a) What is the diameter of the image formed by the objective?(b) What angle is subtended by the final image at
The objective lens of the refracting telescope at the Yerkes Observatory has a focal length of 19.5 m. When it is used to look at the moon, which subtends an angle of about 0.009 rad, what is the diameter of the image of the moon formed by the objective?
The 200-in (5.1-m) mirror of the reflecting telescope at Mt. Palomar has a focal length of 1.68 m.(a) By what factor is the light-gathering power increased over the 40-in (1.016-m) diameter refracting lens of the Yerkes Observatory telescope?(b) If the focal length of the eyepiece is 1.25 cm, what
An astronomical telescope has a magnifying power of 7. The two lenses are 32 cm apart. Find the focal length of each lens.
A disadvantage of the astronomical telescope for terrestrial use (for example, at a football game) is that the image is inverted. A Galilean telescope uses a converging lens as its objective, but a diverging lens as its eyepiece. The image formed by the objective is behind the eyepiece at its focal
A Galilean telescope (see Problem 94) is designed so that the final image is at the near point, which is 25 cm (rather than at infinity). The focal length of the objective is 100 cm and that of the eyepiece is –5 cm.(a) If the object distance is 30 m, where is the image of the objective?(b) What
A hunter lost in the mountains tries to make a telescope from two lenses of power 2.0 and 6.5 D, and a cardboard tube.(a) What is the maximum possible magnifying power?(b) How long must the tube be?(c) Which lens should be used as the eyepiece? Why?
If you look into the wrong end of a telescope, that is, into the objective, you will see distant objects reduced in size. For a refracting telescope with an objective of focal length 2.25 m and an eyepiece of focal length 1.5 cm, by what factor is the angular size of the object reduced?
Show that a diverging lens can never form a real image from a real object.
A camera uses a positive lens to focus light from an object onto a film. Unlike the eye, the camera lens has a fixed focal length, but the lens itself can be moved slightly to vary the image distance to the image on the film. A telephoto lens has a focal length of 200 mm. By how much must it move
A wide-angle lens of a camera has a focal length of 28 mm. By how much must it move to change from focusing on an object at infinity to one at a distance of 5 m?
A converging lens made of polystyrene (index of refraction, 1.59) has a focal length of 50 cm. One surface is convex with radius of magnitude 50 cm. Find the radius of the second surface. Is it convex or concave?
A thin converging lens of focal length 10 cm is used to obtain an image that is twice as large as a small object. Find the object and image distances if(a) The image is to be erect and(b) The image is to be inverted. Draw a ray diagram for each case.
A scuba diver wears a diving mask with a face plate that bulges outward with a radius of curvature of 0.5 m. There is thus a convex spherical surface between the water and the air in the mask. A fish is 2.5 m in front of the diving mask.(a) Where does the fish appear to be?(b) What is the
You wish to see an image of your face for applying makeup or shaving. If you want the image to be upright, virtual, and magnified 1.5 times when your face is 30 cm from the mirror, what kind of mirror should you use, convex or concave, and what should its focal length be?
A small object is 20 cm from a thin positive lens of focal length 10 cm. To the right of the lens is a plane mirror that crosses the axis at the second focal point of the lens and is tilted so that the reflected rays do not go back through the lens (Figure).(a) Find the position of the final
A 35-mm camera has a picture size of 24 mm by 36 mm. It is used to take a picture of a person 175 cm tall so that the image just fills the height (24 mm) of the film. How far should the person stand from the camera if the focal length of the lens is 50 mm?
A 35-mm camera with interchangeable lenses is used to take a picture of a hawk that has a wing span of 2m. The hawk is 30 m away. What would be the ideal focal length of the lens used so that the image of the wings just fills the width of the film, which is 36 mm?
An object is placed 12 cm to the left of a lens of focal length 10 cm. A second lens of focal length 12.5 cm is placed 20 cm to the right of the first lens.(a) Find the position of the final image.(b) What is the magnification of the image?(c) Sketch a ray diagram showing the final image.
(a) Show that if f is the focal length of a thin lens in air, its focal length in water isWhere nw is the index of refraction of water and n is that of the lens.(b) Calculate the focal length in air and in water of a double -concave lens of index of refraction n = 1.5 that has radii of magnitude 30
(a) Find the focal length of a thick double-convex lens with an index of refraction of 1.5, a thickness of 4 cm, and radii of +20 cm and –20 cm.(b) Find the focal length of this lens in water.
A 2-cm-thick layer of water (n = 1.33) floats on top of a 4-cm-thick layer of carbon tetrachloride (n = 1.46) in a tank. How far below the top surface of the water does the bottom of the tank appear to be to an observer looking from above at normal incidence?
While sitting in your car, you see a jogger in your side mirror, which is convex with a radius of curvature of magnitude 2 m. The jogger is 5 m from the mirror and is approaching at 3.5 m/s. How fast does the jogger appear to be running when viewed in the mirror?
In the seventeenth century, Antonie van Leeuwenhoek, the first great microscopist, used simple spherical lenses made first of water droplets and then of glass for his first instruments. He made staggering discoveries with these simple lenses. Consider a glass sphere of radius 2.0 mm with an index
An object is 15 cm to the left of a thin convex lens of focal length 10 cm. A concave mirror of radius 10 cm is 25 cm to the right of the lens.(a) Find the position of the final image formed by the mirror and lens.(b) Is the image real or virtual? Erect or inverted?(c) Show on a diagram where your
When a bright light source is placed 30 cm in front of a lens, there is an erect image 7.5 cm from the lens. There is also a faint inverted image 6 cm in front of the lens due to reflection from the front surface of the lens. When the lens is turned around, this weaker, inverted image is 10 cm in
A horizontal concave mirror with radius of curvature of 50 cm holds a layer of water with an index of refraction of 1.33 and a maximum depth of 1 cm. At what height above the mirror must an object be placed so that its image is at the same position as the object?
A lens with one concave side with a radius of magnitude 17 cm and one convex side with a radius of magnitude 8 cm has a focal length in air of 27.5 cm. When placed in a liquid with an unknown index of refraction, the focal length increases to 109 cm. What is the index of refraction of the liquid?
A glass ball of radius 10 cm has an index of refraction of 1.5. The back half of the ball is silvered so that it acts as a concave mirror (Figure). Find the position of the final image seen by an eye to the left of the object and ball for an object at(a) 30 cm and(b) 20 cm to the left of the front
(a) Show that a small change dn in the index of refraction of a lens material produces a small change in the focal length df given approximately by df/f = –dn/(n – 1).(b) Use this result to find the focal length of a thin lens for blue light, for which n = 1.53, if the focal length for red
The lateral magnification of a spherical mirror or a thin lens is given by m = –s’/s. Show that for objects of small horizontal extent, the longitudinal magnification is approximately –m2.
(Multiple choice)(1) True or False(a) The virtual image formed by a concave mirror is always smaller than the object.(b) A concave mirror always forms a virtual image.(c) A convex mirror never forms a real image of a real object.(d) A concave mirror never forms an enlarged real image of an
1. Can a virtual image be photographed?2. Answer Problem 9 for a convex mirror.
1. The focal length of a simple lens is different for different colors of light. Why?2. A bird above the water is viewed by a scuba diver submerged beneath the water's surface directly below the bird. Does the bird appear to the diver to be closer to or farther from the surface than it actually
1. Show that when the image of a simple magnifier is viewed at the near point, the lateral and angular magnification of the magnifier are equal.2. Find the final image for the situation in Problem 108 when the mirror is not tilted. Assume that the image is viewed by an eye to the left of the object
(a) What minimum path difference is needed to introduce a phase shift of 180in light of wavelength 600 nm?(b) What phase shift will that path difference introduce in light of wavelength 800 nm?
Light of wavelength 500 nm is incident normally on a film of water 10–4 cm thick. The index of refraction of water is 1.33.(a) What is the wavelength of the light in the water?(b) How many wavelengths are contained in the distance 2t, where t is the thickness of the film?(c) What is the phase
Two coherent microwave sources that produce waves of wavelength 1.5 cm are in the xy plane, one on the y axis at y = 15 cm and the other at x = 3 cm, y = 14 cm. If the sources are in phase, find the difference in phase between the two waves from these sources at the origin.
A loop of wire is dipped in soapy water and held so that the soap film is vertical.(a) Viewed by reflection with white light, the top of the film appears black. Explain why.(b) Below the black region are colored bands. Is the first band red or violet?(c) Describe the appearance of the film when it
A wedge-shaped film of air is made by placing a small slip of paper between the edges of two flat plates of glass. Light of wavelength 700 nm is incident normally on the glass plates, and interference bands are observed by reflection.(a) Is the first band near the point of contact of the plates
The diameters of fine wires can be accurately measured using interference patterns. Two optically flat pieces of glass of length L are arranged with the wire between them as shown in Figure. The setup is illuminated by monochromatic light, and the resulting interference fringes are detected.
Light of wavelength 600 nm is used to illuminate normally two glass plates 22 cm in length that touch at one end and are separated at the other end by a wire of radius 0.025 mm. How many bright fringes appear along the total length of the plates?
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