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physics
light and optics

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

Sam purchases +3.50-diopter eyeglasses which correct his faulty vision to put his near point at 25 cm. (assume he wears the lenses 2.0 cm from his eyes.)(a) Calculate the focal length of Sam’s glasses.(b) Calculate Sam’s near point without glasses.(c) Pam, who has normal eyes with near point at
As nearly morning passed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to change the f -number from f /5.6 to f /22. By what factor had the sunlight intensity increased during that time?
Show that for objects very far away (assume infinity), the magnification of a camera lens is proportional to its focal length.
For a camera equipped with a 50-mm-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the film?
A woman can see clearly with her right eye only when objects are between 45 cm and 155 cm away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 cm away (lower part) with her right eye? Assume that the glasses will
A child has a near point of 15 cm. what is the maximum magnification the child can obtain using an 8.0-cm-focal-length magnifier? What magnification can a normal eye obtain with the same lens? Which person sees more detail?
What is the magnifying power of a +4.0-D lens used as a magnifier? Assume a relaxed normal eye.
A physicist lost in the mountains tries to make a telescope using the lens from his reading glasses. They have powers of +2.0 D and +4.5 D, respectively.(a) What maximum magnification telescope is possible?(b) Which lens should be used as the eyepiece?
A 50-year-old man uses +2.5-diopter lenses to read a newspaper 25 cm away. Ten years later, he must hold the paper 35 cm away to see clearly with the same lenses. What power lenses does he need now in order to hold a paper 25 cm away? (Distances are measured from the lens.)
Spy planes fly at extremely high altitudes (25 km) to avoid interception. Their cameras are reportedly able to discern features as small as 5 cm. what must be the minimum aperture of the camera lens to afford this resolution? (Use λ = 550 nm.)
When shooting pictures at very short distances, exposure time must be increased because of the increased distance of the lens from the film for a focused image.(a) show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four
The objective lens and the eyepiece of a telescope are spaced 85 cm apart. If the eyepiece is +23 diopters, what is the total magnification of the telescope?
The Hubble space telescope, with an objective diameter of 2.4m, is viewing the moon. Estimate the minimum distance between two objects on the moon that the Hubble can distinguish. Consider diffraction of light of wavelength 550nm. Assume the Hubble is near the earth.
Two converging lenses, one with f = 4.0cm and the other with f = 44 cm, are made into a telescope.(a) What are the length and magnification? Which lens should be the eyepiece?(b) Assume these lenses are now combined to make a microscope; if the magnification needs to be 25X, how long would the
An astronomical telescope has a magnification of 8.0. If the two lenses are 28 cm apart, determine the focal length of each lens.
You want to design a spy satellite to photograph license plate number. Assuming it is necessary to resolve points separated by 5 cm with 550-nm light, and that the satellite orbits at a height of 130 km, what minimum lens aperture (diameter) is required?
A Lucite planoconvex lens (Fig. 23-29a) has one flat surface and the other has R = 18.4 cm. this lens is used to view an object, located 66.0 cm away from the lens, which is a mixture of red and yellow. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What
Why is the depth of field greater, and the image sharper, when a camera lens is “stopped down’’ to a larger f – number? Ignore diffraction.
Describe how diffraction effects the statement of question 1.
Why must a camera lens be moved farther from the film to focus on a closer object?
Why are bifocals needed mainly by older persons and not generally by younger people?
Will a nearsighted person who wears corrective lenses in her glasses be able to see clearly underwater when wearing those glasses? Use a diagram to show why or why not.
You can tell whether a person is nearsighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. 25-47), is the person farsighted or nearsighted?
In attempting to discern distant details, people will sometimes squint. Why does this help?
Is the image formed on the retina of the human eye upright or inverted? Discuss the implications of this for our perception of objects.
The human eye is much like a camera- yet, when a camera shutter is left open and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.
Reading glasses use converging lenses. A simple magnifier is also a converging lens. Are reading glasses therefore magnifiers? Discuss the similarities and differences between converging lenses and used for these two different purposes.
Inexpensive microscopes for children’s use usually produce images that are colored at the edges. Why?
Spherical aberration in a thin lens is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should face the object? Use ray diagrams to show why.
Which aberrations present in a simple lens are not present (or are greatly reduced) in the human eye?
Explain why chromatic aberration occurs for thin lenses but not for mirrors.
By what factor can you improve resolution, other things being equal, if you use blue light (λ = 450 nm) rather than red (700 nm)?
Give at least two advantages for the use of large reflecting mirrors in astronomical telescopes.
Which color of visible light would give the best resolution in a microscope? Explain.
Atoms have diameters of about 10-8 cm. can visible light be used to ‘’see’’ an atom? Explain.
What would be the appearance of the Moon if it had?(a) A rough surface;(b) A polished mirror like surface?
Archimedes is said to have burned the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with huge spherical mirror. Is this reasonable?
Although a plane mirror appears to reverse left and right, id doesn’t reverse up and down. Explain.
If a concave mirror produces a real image is the image necessarily inverted? Explain.
An object is placed along the principal axis of a spherical mirror. The magnification of the object is – 3.0. Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?
Using the rules for the three rays discussed with reference to Fig. 23-13, draw ray 2 for Fig. 23-17b.
What is the focal length of a plane mirror? What is the magnification of a plane mirror?
When you look at the Moon€™s reflection from a ripply sea, it appears elongated (Fig. 23-44). Explain
What is the angle of refraction when a light ray meets the boundary between two materials perpendicularly?
How might you determine the speed of light in a solid, rectangular, transparent object?
When you look down into a swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams).
Your eye looks into an aquarium and views a fish inside. One ray of light that emerges from the tank is shown in Fig. 23-45, as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.
How can you “see” a round drop of water on a table even though the water is transparent and colorless?
When you look up at an object in air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it directly in air? Explain.
How can a spherical mirror have negative object distance?
Draw a ray diagram to show why a stick looks bent when part of it is under water (Fig. 23-21)
Light rays from stars (including our Sun) always bend toward the vertical direction as they pass through the Earth’s atmosphere. (a) Why does this make sense?(b) What can you conclude about the apparent positions of stars as viewed from Earth?
Where must the film be placed if a camera lens is to make a sharp image of an object very far away?
What type of mirror is shown in Fig. 23-46? Explain.
A photographer moves closer to his subject and then refocuses. Does the camera lens move farther from or closer to the film? Explain.
Can a diverging lens form a real image under any circumstances? Explain.
Use ray diagrams to show that a real image formed by a thin lens is always inverted. Whereas a virtual images is always upright if the object is real.
Light rays are said to be “reversible” is this consistent with the thin lens equation? Explain.
Can real images be projected on a screen? Can virtual images? Can either be photographed? Discuss carefully.
A thin converging lens is moved closer to a nearby object. Does the real image formed change(a) In Position,(b) In Size? If yes, describe how.
A lens is made of a material with an index of refraction n = 1.30. In air, it is a converging lens. Will it still be a converging lens if placed in water? Explain, using a ray diagram.
A dog with its tail in the air stands facing a converging lens. If the nose and the tail are each focused on a screen in turn, which will have the grater magnification?
A cat with its tail in the air stands facing converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?
Why, in Example 23-13, must the converging lens have a shorter focal length than the diverging lens if the latter’s focal length is to be determined by combining them?
Explain how you could have a virtual object.
An unsymmetrical lens (says, Plano convex) forms and image of a nearby object, does the image point change if the lens is turned around?
The thicker a double convex lens is in the center as compared to its edges, the shorter its focal length for a given lens diameter. Explain.
Consider two converging lenses separated by some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image if so, where if not, why not?
Suppose that you want to take a photograph of your self as you look at your image in a flat mirror 2.5m away. For what distance should the camera lens be focused?
When you look at yourself in a 60-cm-tall plane mirror, your see the same amount of you body whether you are close to the mirror or far away. (Try it and see). Use ray diagrams to show why this should be true.
Two mirrors meet at a 135o angle, Fig. 23-47. If light rays strike one mirror at 40o as shown, at what angle Ф do they leave the second mirror?
A person whose eyes are 1.68 m above the floor stands 2.20 m is front of a vertical plane mirror whose bottom edge is 43 cm above the floor, Fig. 23-48. What is supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?
Suppose you are 90cm from a plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5mm?
Show that if two plane mirrors meet at an angle Ф, a single ray reflected successively from both mirrors is deflected through an angle of 2Ф independent of the incident angle. Assume Ф < 90o and those only two reflections, one from each mirror, take place.
A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which mirror was made?
How far from a concave mirror (radius 23.0cm) must ab object be placed if its image is to be at infinity?
If you look at yourself in shiny Christmas tree ball with a diameter of 9.0 cm when you face is 30.0cm away from it, where is your image? Is it real or virtual? Is it upright or inverted?
A mirror at an amusement park shows and upright image of any person who stand 1.4 m in front of it if the image is three times the person’s height, what is the radius of curvature?
A dentist wants a small mirror that, when 2.20 cm from a tooth, will produce a 4.5 x upright image. What kind of mirror must be used and what must its radius of curvature be?
Some rearview mirrors produce images of cars behind you that are smaller that they would be if the mirror were flat. Are the mirrors concave or convex? What is the mirror’s radius of curvature if cars 20.0m away appear 0.33 x their normal size?
A luminous object 3.0 mm high is placed 20.0 cm from a convex mirror of radius of curvature 20.0cm.(a) Show by ray tracing that the image is virtual, and estimate the image distance.(b) Show that the (negative) image distance can be computed from Eq. 23-2 using a focal length of –10.0cm. (c)
You are standing 3.0 m from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirror.
(a) Where should an object be placed in front of a concave mirror so that it produces an image at the same location as the object? (b) Is the image real or virtual?:(c) Is the image inverted or upright?(d) What is the magnification of the image?
The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 18.0cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
Use two different techniques,(a) A ray diagram, and (b) The mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature C (do > r), and is greater than 1 if the object is within C (do < r).
Show, using a ray diagram, that the magnification m of a convex mirror is m = – di / do, just as for a concave mirror.
Use ray diagrams to show that the mirror equation, Eq. 23-2, is valid for a convex mirror as long as f is considered negative.
The magnification of a convex mirror is + 0.65 x for objects 2.2m from the mirror. What is the focal length of this mirror?
A 4.5-cm-tall object is placed 28cm in front of a spherical mirror. It is desired to produce a virtual image that is upright and 3.5 cm tall. (a) What type of mirror should be used?(b) Where is the image located?(c) What is the focal length of the mirror?(d) What is the radius of curvature of the
A shaving/makeup mirror is designed to magnify your face be a factor of 1.33 when your face is placed 20.0 cm in front of it.(a) What type of mirror is it?(b) Describe the type of image that it makes of your face.(c) Calculate the required radius of curvature for the mirror.
What is the speed of light in? (a) Crown glass, (b) Lucite, and (c) Ethyl alcohol?
The speed of light in ice is 2.29 x 108m/s. What is the index of refraction of ice?
The speed of light in a certain substance is 89% of its value in water. What is the index of refraction of this substance?
A flashlight beam strikes the surface of a pane of glass (n = 1.58) at a 63o angle to the normal. What is the angle of refraction?
A diver shines a flashlight upward from beneath the water at a 42.5o angle to the vertical. At what angle does the light leave the water?
A light beam coming from an underwater spotlight exits the water at an angle of 66.0o to the vertical. At what angle of incidence does it hit the air-water interface from below the surface?
Rays of the Sun are seen to make a 31.0o angle to the vertical beneath the water. At what angle above the horizon is the Sun?
An aquarium filled with water has flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5o angle to the perpendicular (Fig. 23-49). What is the angle of this light ray when it enters?(a) The glass, and then(b) The water?(c) What
In searching the bottom of a pool at night, a watchman shines a narrow beam of light from his flash-light, 1.3m above the water level, onto the surface of the water at a point 2.7m from the edge of the pool (Fig.23-50). Where does the spot of light hit the bottom of the pool measured from the wall
Light is incident on an equilateral glass prism at a 45.0o angle to one face, Fig. 23-51. Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.

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