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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

A converging lens made of glass (n = 1.5) is placed under water (n = 1.33). Describe how the focal length of the lens under water compares to the focal length in air. Draw a diagram to illustrate your answer.
An object 8.0 cm high forms a virtual image 3.5 cm high located 4.0 cm behind a mirror. (a) Find the object distance. (b) Describe the mirror: is it plane, convex, or concave? (c) What are its focal length and radius of curvature?
A point source of light is placed 10 cm in front of a concave mirror; the reflected rays are parallel. What is the radius of curvature of the mirror?
A glass prism bends a ray of blue light more than a ray of red light since its index of refraction is slightly higher for blue than for red. Does a diverging glass lens have the same focal point for blue light and for red light? If not, for which color is the focal point closer to the lens?
A laser beam is traveling through an unknown substance. When it encounters a boundary with air, the angle of reflection is 25.0 ° and the angle of refraction is 37.0°. (a) What is the index of refraction of the substance? (b) What is the speed of light in the substance? (c) At what minimum angle
A scuba diver in a lake aims her underwater spotlight at the lake surface. (a) If the beam makes a 75° angle of incidence with respect to a normal to the water surface, is it reflected, transmitted, or both? Find the angles of the reflected and transmitted beams (if they exist). (b) Repeat for a
Two plane mirrors form a 70.0° angle as shown. For what angle Î¸ is the final ray horizontal?
Xi Yang is practicing for his driver's license test. He notices in the rearview mirror that a tree, located directly behind the automobile, is approaching his car as he is backing up. If the car is moving at 8.0 km/h in reverse, how fast relative to the car does the image of the tree appear to be
A plane mirror reflects a beam of light. Show that the rotation of the mirror by an angle a causes the beam to rotate through an angle 2a.
A 3.00-cm-high pin, when placed at a certain distance in front of a concave mirror, produces an upright image 9.00 cm high, 30.0 cm from the mirror. Find the position of the pin relative to the mirror and the image. Draw a ray diagram to illustrate.
A dentist holds a small mirror 1.9 cm from a surface of a patient's tooth. The image formed is upright and 5.0 times as large as the object. (a) Is the image real or virtual? (b) What is the focal length of the mirror? Is it concave or convex? (c) If the mirror is moved closer to the tooth, does
An object of height 5.00 cm is placed 20.0 cm from a converging lens of focal length 15.0 cm. Draw a ray diagram to find the height and position of the image.
A letter on a page of the compact edition of the Oxford English Dictionary is 0.60 mm tall. A magnifying glass (a single thin lens) held 4.5 cm above the page forms an image of the letter that is 2.4 cm tall. (a) Is the image real or virtual? (b) Where is the image? (c) What is the focal length of
An object is placed 10.0 cm in front of a lens. An upright, virtual image is formed 30.0 cm away from the lens. What is the focal length of the lens? Is the lens converging or diverging?
A manufacturer is designing a shaving mirror, which is intended to be held close to the face. If the manufacturer wants the image formed to be upright and as large as possible, what characteristics should he choose? (type of mirror? long or short focal length relative to the object distance of face
The focal length of a thin lens is ˆ’ 20.0 cm. A screen is placed 160 cm from the lens. What is the y -coordinate of the point where the light ray shown hits the screen? The incident ray is parallel to the central axis and is cm from that axis.
A ray of light is reflected from two mirrored surfaces as shown in the figure. If the initial angle of incidence is 34°, what are the values of angles Î± and Î²? (The figure is not to scale.)
Choose two rays in Fig. 23.7 and use them to prove that the angle of incidence is equal to the angle of reflection
A beam of light consisting of a mixture of red, yellow, and blue light originates from a source submerged in some carbon disulfide. The light beam strikes an interface between the carbon disulfide and air at an angle of incidence of 37.5° as shown in the figure. The carbon disulfide has the
A concave mirror has a radius of curvature of 14 cm. If a point like object is placed 9.0 cm away from the mirror on its principal axis, where is the image?
A glass block (n = 1.7) is submerged in an unknown liquid. A ray of light inside the block undergoes total internal reflection. What can you conclude concerning the index of refraction of the liquid?
Ray diagrams often show objects that conveniently have one end on the principal axis. Draw a ray diagram and locate the image for the object shown in the figure that extends beyond the principal axis.
A 5.0-cm-tall object is placed 50.0 cm from a lens with focal length − 20.0 cm. (a) How tall is the image? (b) Is the image upright or inverted?
A ray of light in air is incident at an angle of 60.0 ° with the surface of some benzene contained in a shallow tank made of crown glass. What is the angle of refraction of the light ray when it enters the glass at the bottom of the tank?
A ray of light passes from air through dense flint glass and then back into air. The angle of incidence on the first glass surface is 60.0°. The thickness of the glass is 5.00 mm; its front and back surfaces are parallel. How far is the ray displaced as a result of traveling through the glass?
Show that the deviation angle d for a ray striking a thin converging lens at a distance d from the principal axis is given by δ = d / f. Therefore, a ray is bent through an angle d that is proportional to d and does not depend on the angle of the incident ray (as long as it is paraxial).
Why must a camera or a slide projector use a converging lens? Why must the objective of a microscope or telescope be a converging lens (or a converging mirror)? Why can the eyepiece of a telescope be either converging or diverging?
For human eyes, about 70% of the refraction occurs at the cornea; less than 25% occurs at the two surfaces of the lens. Why?
What are some of the advantages of using mirrors rather than lenses for astronomical telescopes?
When snorkeling, you wear goggles in order to see clearly. Why is your vision blurry without the goggles? A nearsighted person notices that he is able to see nearby objects more clearly when he is underwater (without goggles or corrective lenses) than in air (without corrective lenses). Why might
When the muscles of the eye remain tensed for a significant period of time, eyestrain results how much is this a concern for a person using? (a) A microscope, (b) A telescope, (c) A simple magnifier.
Both a microscope and a telescope can be constructed from two converging lenses. What are the differences? Why can't a telescope be used as a microscope? Why can't a microscope be used as a telescope?
In her bag, a photographer is carrying three exchangeable camera lenses with focal lengths of 400.0 mm, 50.0 mm, and 28.0 mm. Which lens should she use for? (a) Wide angle shots (a cathedral, taken from the square in front), (b) Everyday use (children at play), (c) Telephoto work (lions in Africa
The figure shows a schematic diagram of a defective eye. What is this defect called?
A magnifying glass can be held over a piece of white paper and its position adjusted until the image of an overhead light is formed on the paper. Explain.
Why is a refracting telescope with a large angular magnification longer than one with a smaller magnification?
Why are astronomical observatories often located on mountaintops?
Why do some telescopes produce an inverted image?
Why is the receiving antenna of a satellite dish placed at a set distance from the dish?
Two magnifying glasses are labeled with their angular magnifications. Glass A has a magnification of "2 ×" (M = 2) and glass B has a magnification of 4 ×. Which has the longer focal length? Explain.
What causes chromatic aberration? What can be done to compensate for chromatic aberration?
An object is placed 12.0 cm in front of a lens of focal length 5.0 cm. Another lens of focal length 4.0 cm is placed 2.0 cm past the first lens. (a) Where is the final image? Is it real or virtual? (b) What is the overall magnification?
You plan to project an inverted image 30.0 cm to the right of an object. You have a diverging lens with focal length − 4.00 cm located 6.00 cm to the right of the object. Once you put a second lens at 18.0 cm to the right of the object, you obtain an image in the proper location. (a) What is the
A camera uses a 200.0-mm focal length telephoto lens to take pictures from a distance of infinity to as close as 2.0 m. What are the minimum and maximum distances from the lens to the film?
Kim says that she was less than 10 ft away from the president when she took a picture of him with her 50-mm focal length camera lens. The picture shows the upper half of the president's body (or 3.0 ft of his total height). On the negative of the film, this part of his body is 18 mm high. How close
A statue is 6.6 m from the opening of a pinhole camera, and the screen is 2.8 m from the pinhole. (a) Is the image erect or inverted? (b) What is the magnification of the image? (c) To get a brighter image, we enlarge the pinhole to let more light through, but then the image looks blurry.
Esperanza uses a 35-mm camera with a standard lens of focal length 50.0 mm to take a photo of her son Carlos, who is 1.2 m tall and standing 3.0 m away. (a) What must be the distance between the lens and the film to get a properly focused picture? (b) What is the magnification of the image? (c)
A person on a safari wants to take a photograph of a hippopotamus from a distance of 75.0 m. The animal is 4.00 m long and its image is to be 1.20 cm long on the film. (a) What focal length lens should be used? (b) What would be the size of the image if a lens of 50.0-mm focal length were used?
Jim plans to take a picture of McGraw Tower with a 35-mm camera that has a 50.0-mm focal length lens. A roll of 35-mm film is 35 mm wide; each frame is 24 mm by 36 mm. The tower has a height of 52 m and Jim wants a detailed close-up picture. How close to the tower should Jim be to capture the
A photographer wishes to take a photograph of the Eiffel Tower (300 m tall) from across the Seine River, a distance of 300 m from the tower. What focal length lens should she use to get an image that is 20 mm high on the film?
If a slide of width 36 mm (see the figure with Problem 16) is to be projected onto a screen of 1.50 m width located 12.0 m from the projector, what focal length lens is required to fill the width of the screen?In Problem 16
A slide projector has a lens of focal length 12 cm. Each slide is 24 mm by 36 mm (see the figure with Problem 16). The projector is used in a room where the screen is 5.0 m from the projector. How large must the screen be?
A converging lens and a diverging lens, separated by a distance of 30.0 cm, are used in combination. The converging lens has a focal length of 15.0 cm. The diverging lens is of unknown focal length. An object is placed 20.0 cm in front of the converging lens; the final image is virtual and is
A converging lens with focal length 3.00 cm is placed 4.00 cm to the right of an object. A diverging lens with focal length − 5.00 cm is placed 17.0 cm to the right of the converging lens. (a) At what location(s), if any, can you place a screen in order to display an image? (b) Repeat part (a)
A converging lens with a focal length of 3.00 cm is placed 24.00 cm to the right of a concave mirror with a focal length of 4.00 cm. An object is placed between the mirror and the lens, 6.00 cm to the right of the mirror and 18.00 cm to the left of the lens. Name three places where you could find
If the distance from the lens system (cornea + lens) to the retina is 2.00 cm, show that the focal length of the lens system must vary between 1.85 cm and 2.00 cm to see objects from 25.0 cm to infinity.
Suppose that the lens system (cornea + lens) in a particular eye has a focal length that can vary between 1.85 cm and 2.00 cm, but the distance from the lens system to the retina is only 1.90 cm. (a) Is this eye nearsighted or farsighted? Explain. (b) What range of distances can the eye see clearly
If Michaela needs to wear reading glasses with refractive power of +3.0 D, what is her uncorrected near point? Neglect the distance between the glasses and the eye.
The uncorrected far point of Colin's eye is 2.0 m. What refractive power contact lens enables him to clearly distinguish objects at large distances?
The distance from the lens system (cornea + lens) of a particular eye to the retina is 1.75 cm. What is the focal length of the lens system when the eye produces a clear image of an object 25.0 cm away?
A nearsighted man cannot clearly see objects more than 2.0 m away. The distance from the lens of the eye to the retina is 2.0 cm, and the eye's power of accommodation is 4.0 D (the focal length of the cornea-lens system increases by a maximum of 4.0 D over its relaxed focal length when
Anne is farsighted; the nearest object she can see clearly without corrective lenses is 2.0 m away. It is 1.8 cm from the lens of her eye to the retina. (a) Sketch a ray diagram to show (qualitatively) what happens when she tries to look at something closer than 2.0 m without corrective lenses.
Thomas wants to use his 5.5-D reading glasses as a simple magnifier. What is the angular magnification of this lens when Thomas's eye is relaxed?
Two converging lenses are placed 88.0 cm apart. An object is placed 1.100 m to the left of the first lens, which has a focal length of 25.0 cm. The final image is located 15.0 cm to the right of the second lens. (a) What is the focal length of the second lens? (b) What is the total magnification?
(a) What is the focal length of a magnifying glass that gives an angular magnification of 8.0 when the image is at infinity? (b) How far must the object be from the lens? Assume the lens is held close to the eye.
Keesha is looking at a beetle with a magnifying glass. She wants to see an upright, enlarged image at a distance of 25 cm. The focal length of the magnifying glass is + 5.0 cm. Assume that Keesha's eye is close to the magnifying glass. (a) What should be the distance between the magnifying glass
Callum is examining a square stamp of side 3.00 cm with a magnifying glass of refractive power + 40.0 D. The magnifier forms an image of the stamp at a distance of 25.0 cm. Assume that Callum's eye is close to the magnifying glass.(a) What is the distance between the stamp and the magnifier?(b)
A simple magnifying glass can focus sunlight enough to heat up paper or dry grass and start a fire. A magnifying glass with a diameter of 4.0 cm has a focal length of 6.0 cm. (a) Using the information found on the inside back cover of the book; estimate the size of the image of the Sun when the
An insect that is 5.00 mm long is placed 10.0 cm from a converging lens with a focal length of 12.0 cm. (a) What is the position of the image? (b) What is the size of the image? (c) Is the image upright or inverted? (d) Is the image real or virtual? (e) What is the angular magnification if the
A simple magnifier gives the maximum angular magnification when it forms a virtual image at the near point of the eye instead of at infinity. For simplicity, assume that the magnifier is right up against the eye, so that distances from the magnifier are approximately the same as distances from the
The figure shows a schematic diagram of a microscope. For the object and image locations showed, which of the points (A, B, C, or D) represents a focal point of the eyepiece? Draw a ray diagram.
The eyepiece of a microscope has a focal length of 1.25 cm and the objective lens focal length is 1.44 cm. (a) If the tube length is 18.0 cm, what is the angular magnification of the microscope? (b) What objective focal length would be required to double this magnification?
Jordan is building a compound microscope using an eyepiece with a focal length of 7.50 cm and an objective with a focal length of 1.500 cm. He will place the specimen a distance of 1.600 cm from the objective. (a) How far apart should Jordan place the lenses? (b) What will be the angular
The wing of an insect is 1.0 mm long. When viewed through a microscope, the image is 1.0 m long and is located 5.0 m away. Determine the angular magnification.
A converging lens with a focal length of 15.0 cm and a diverging lens are placed 25.0 cm apart, with the converging lens on the left. A 2.00-cm-high object is placed 22.0 cm to the left of the converging lens. The final image is 34.0 cm to the left of the converging lens. (a) What is the focal
A microscope has an eyepiece that gives an angular magnification of 5.00 for a final image at infinity and an objective lens of focal length 15.0 mm. The tube length of the microscope is 16.0 cm. (a) What is the transverse magnification due to the objective lens alone? (b) What is the angular
Repeat Problem 40 using a different eyepiece that gives an angular magnification of 5.00 for a final image at the viewer's near point (25.0 cm) instead of at infinity. In problem 40 How far from the objective should the object be placed?
A microscope has an objective lens of focal length 5.00 mm. The objective forms an image 16.5 cm from the lens. The focal length of the eyepiece is 2.80 cm. (a) What is the distance between the lenses? (b) What is the angular magnification? The near point is 25.0 cm. (c) How far from the
Repeat Problem 42 if the eyepiece location is adjusted slightly so that the final image is at the viewer's near point (25.0 cm) instead of at infinity.
Use the thin-lens equation to show that the transverse magnification due to the objective of a microscope is m o = − L / fo.
(a) If you were stranded on an island with only a pair of 3.5-D reading glasses, could you make a telescope? If so, what would be the length of the telescope and what would be the best possible angular magnification? (b) Answer the same questions if you also had a pair of 1.3-D reading glasses.
A telescope mirror has a radius of curvature of 10.0 m. It is used to take a picture of the Moon. What is the diameter of the image of the Moon produced by this mirror? (See the inside back cover for necessary information.)
(a) What is the angular size of the Moon as viewed from Earth's surface? See the inside back cover for necessary information. (b) The objective and eyepiece of a refracting telescope have focal lengths 80 cm and 2.0 cm, respectively. What the angular size of the Moon is as viewed through this
What is the distance between the objective and eyepiece in the Yerkes telescope?
You have a set of converging lenses with focal lengths 1.00 cm, 10.0 cm, 50.0 cm, and 80.0 cm. (a) Which two lenses would you select to make a telescope with the largest magnifying power? What is the angular magnification of the telescope when viewing a distant object? (b) Which lens is used as
An object is located 16.0 cm in front of a converging lens with focal length 12.0 cm. To the right of the converging lens, separated by a distance of 20.0 cm, is a diverging lens of focal length -10.0 cm. Find the location of the final image by ray tracing and verify using the lens equations.
A refracting telescope is 45.0 cm long and the caption states that the telescope magnifies images by a factor of 30.0. Assuming these numbers are for viewing an object an infinite distance away with minimum eyestrain, what is the focal length of each of the two lenses?
The objective lens of an astronomical telescope forms an image of a distant object at the focal point of the eyepiece, which has a focal length of 5.0 cm. If the two lenses are 45.0 cm apart, what is the angular magnification?
A refracting telescope is used to view the Moon. The focal lengths of the objective and eyepiece are + 2.40 m and + 16.0 cm, respectively. (a) What should be the distance between the lenses? (b) What is the diameter of the image produced by the objective? (c) What is the angular magnification?
Good lenses used in cameras and other optical devices are actually compound lenses, made of five or more lenses put together to minimize distortions, including chromatic aberration. Suppose a converging lens with a focal length of 4.00 cm is placed right next to a diverging lens with focal length
Two converging lenses, separated by a distance of 50.0 cm, are used in combination. The first lens, located to the left, has a focal length of 15.0 cm. The second lens, located to the right, has a focal length of 12.0 cm. An object, 3.00 cm high, is placed at a distance of 20.0 cm in front of the
A camera has a telephoto lens of 240-mm focal length. The lens can be moved in and out a distance of 16 mm from the film plane by rotating the lens barrel. If the lens can focus objects at infinity, what is the closest object distance that can be focused?
You have two lenses of focal length 25.0 cm (lens 1) and 5.0 cm (lens 2). (a) To build an astronomical telescope that gives an angular magnification of 5.0, how should you use the lenses (which for objective and which for eyepiece)? Explain. (b) How far apart should they be?
The Ortiz family is viewing slides from their summer vacation trip to the Grand Canyon. Their slide projector has a projection lens of 10.0-cm focal length and the screen is located 2.5 m from the projector.(a) What is the distance between the slide and the projection lens?(b) What is the
A slide projector, using slides of width 5.08 cm, produces an image that is 2.00 m wide on a screen 3.50 m away. What is the focal length of the projector lens?
An object is located 10.0 cm in front of a converging lens with focal length 12.0 cm. To the right of the converging lens is a second converging lens, 30.0 cm from the first lens, of focal length 10.0 cm. Find the location of the final image by ray tracing and verify by using the lens equations.
An object is placed 20.0 cm from a converging lens with focal length 15.0 cm (see the figure, not drawn to scale). A concave mirror with focal length 10.0 cm is located 75.0 cm to the right of the lens.(a) Describe the final image is it real or virtual upright or inverted?(b) What is the location
Two lenses, of focal lengths 3.0 cm and 30.0 cm, are used to build a small telescope. (a) Which lens should be the objective? (b) What is the angular magnification? (c) How far apart are the two lenses in the telescope?
(a) If Harry has a near point of 1.5 m, what focal length contact lenses does he require? (b) What is the power of these lenses in diopters?
An astronomical telescope provides an angular magnification of 12. The two converging lenses are 66 cm apart. Find the focal length of each of the lenses.

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