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physics
light and optics
Questions and Answers of
Light and Optics
A contact lens is made of plastic with an index of refraction of 1.50. The lens has an outer radius of curvature of + 2.00 cm and an inner radius of curvature of + 2.50 cm. What is the focal length
The left face of a biconvex lens has a radius of curvature of 12.0 cm, and the right face has a radius of curvature of 18.0 cm. The index of refraction of the glass is 1.44.(a) Calculate the focal
A converging lens has a focal length of 20.0 cm. Locate the images for object distances of(a) 40.0 cm, (b) 20.0 cm, and (c) 10.0 cm. For each case, state whether the image is real or virtual and
Where must an object be placed to have unit magnification (|M| =1.00) (a) For a converging lens of focal length 12.0 cm? (b) For a diverging lens of focal length 12.0 cm?
A diverging lens has a focal length of 20.0 cm. Locate the images for object distances of(a) 40.0 cm,(b) 20.0 cm, and(c) 10.0 cm. For each case, state whether the image is real or virtual and upright
The use of a lens in a certain situation is described by the Equation Determine(a) The object distance and (b) The image distance. (c) Use a ray diagram to obtain a description of the image. (d)
A transparent photographic slide is placed in front of a converging lens with a focal length of 2.44 cm. The lens forms an image of the slide 12.9 cm from it. How far is the lens from the slide if
The nickel??s image in figure has twice the diameter of the nickel when the lens is 2.84 cm from the nickel. Determine the focal length of thelens.
A certain LCD projector contains a single thin lens. An object 24.0 mm high is to be projected so that its image fills a screen 1.80 m high. The object-to-screen distance is 3.00 m. (a) Determine the
A person uses a converging lens that has a focal length of 12.5 cm to inspect a gem. The lens forms a virtual image 30.0 cm away. Determine the magnification. Is the image upright or inverted?
A diverging lens is to be used to produce a virtual image one-third as tall as the object. Where should the object be placed?
An object is 5.00 m to the left of a flat screen. A converging lens for which the focal length is f = 0.800 m is placed between object and screen. (a) Show that there are two lens positions that form
A converging lens is placed 30.0 cm to the right of a diverging lens of focal length 10.0 cm. A beam of parallel light enters the diverging lens from the left, and the beam is again parallel when it
An object is placed 20.0 cm to the left of a converging lens of focal length 25.0 cm. A diverging lens of focal length 10.0 cm is 25.0 cm to the right of the converging lens. Find the position and
Two converging lenses, each of focal length 15.0 cm, are placed 40.0 cm apart, and an object is placed 30.0 cm in front of the first lens. Where is the final image formed, and what is the
Object O1 is 15.0 cm to the left of a converging lens with a 10.0-cm focal length. A second lens is positioned 10.0 cm to the right of the first lens and is observed to form a final image at the
A 1.00-cm-high object is placed 4.00 cm to the left of a converging lens of focal length 8.00 cm. A diverging lens of focal length – 16.00 cm is 6.00 cm to the right of the converging lens. Find
Two converging lenses having focal lengths of 10.0 cm and 20.0 cm are placed 50.0 cm apart, as shown in figure. The final image is to be located between the lenses, at the position indicated.(a) How
Lens L1 in Figure has a focal length of 15.0 cm and is located a fixed distance in front of the film plane of a camera. Lens L2 has a focal length of 13.0 cm, and its distance d from the film plane
Consider two thin lenses, one of focal length f1 and the other of focal length f2, placed in contact with each other as shown in figure. Apply the thin-lens equation to each of these lenses and
An object placed 10.0 cm from a concave spherical mirror produces a real image 8.00 cm from the mirror. If the object is moved to a new position 20.0 cm from the mirror, what is the position of the
An object is placed 12 cm to the left of a diverging lens of focal length – 6.0 cm. A converging lens of focal length 12 cm is placed a distance d to the right of the diverging lens. Find the
A convergent lens with a 50.0-mm focal length is used to focus an image of a very distant scene onto a flat screen 35.0 mm wide. What is the angular width α of the scene included in the image on the
The object in figure is midway between the lens and the mirror. The mirror??s radius of curvature is 20.0 cm, and the lens has a focal length of _16.7 cm. Considering only the light that leaves the
The lens and mirror in figure are separated by 1.00 m and have focal lengths of + 80.0 cm and ?? 50.0 cm, respectively. If an object is placed 1.00 m to the left of the lens, locate the final image.
A diverging lens (n = 1.50) is shaped like that in Active figure c. The radius of the first surface is 15.0 cm, and that of the second surface is 10.0 cm.(a) Find the focal length of the lens.
A parallel beam of light enters a glass hemisphere perpendicular to the flat face, as shown in figure. The radius of the hemisphere is R = 6.00 cm, and the index of refraction is n = 1.560. Determine
A converging lens of focal length 20.0 cm is separated by 50.0 cm from a converging lens of focal length 5.00 cm.(a) Find the position of the final image of an object placed 40.0 cm in front of the
To work this problem, use the fact that the image formed by the first surface becomes the object for the second surface. Figure shows a piece of glass with index of refraction 1.50. The ends are
In a darkened room, a burning candle is placed 1.50 m from a white wall. A lens is placed between candle and wall at a location that causes a larger, inverted image to form on the wall. When the lens
An object 2.00 cm high is placed 40.0 cm to the left of a converging lens having a focal length of 30.0 cm. A diverging lens having a focal length of – 20.0 cm is placed 110 cm to the right of the
A floating strawberry illusion can be produced by two parabolic mirrors, each with a focal length of 7.5 cm, facing each other so that their centers are 7.5 cm apart (Figure). If a strawberry is
Figure shows a converging lens with radii R1 = 9.00 cm and R2 = ?? 11.00 cm, in front of a concave spherical mirror of radius R = 8.00 cm. The focal points (F1 and F2) for the thin lens and the
Find the object distances (in terms of f) for a thin converging lens of focal length f if (a) The image is real and the image distance is four times the focal length; (b) The image is virtual and the
The lens maker??s equation for a lens with index n1 immersed in a medium with index n2 takes the form A thin diverging glass (index = 1.50) lens with R1 = ?? 3.00 m and R2 = ?? 6.00 m is surrounded
An observer to the right of the mirror??lens combination shown in figure sees two real images that are the same size and in the same location. One image is upright and the other is inverted. Both
The lens maker’s equation applies to a lens immersed in a liquid if n in the equation is replaced by n1/n2. Here n1 refers to the refractive index of the lens material and n2 is that of the medium
One method for determining the position of an image, either real or virtual, is by means of parallax. If a finger or another object is placed at the position of the image, as shown in Figure, and the
Explain why a mirror cannot give rise to chromatic aberration.
A solar furnace can be constructed by using a concave mirror to reflect and focus sunlight into the enclosure of a furnace. What factors in the design of the reflecting mirror will guarantee that
1. A common mirage is formed when the air gets gradually cooler as the height above the ground increases. What might happen if the air grows gradually warmer as the height increases? This often
Lenses used in eyeglasses, whether converging or diverging, are always designed such that the middle of the lens curves away from the eye. Why?
1. If a cylinder of solid glass or clear plastic is placed above the words LEAD OXIDE and viewed from the side, as shown in figure, the word LEAD appears inverted, but the word OXIDE does not.
Light from an object passes through a lens and forms a visible image on a screen. If the screen is removed, would you be able to see the image if (a) You remained in your present position? (b) You
An inverted image of an object is viewed on a screen from the side facing a converging lens. An opaque card is then introduced covering only the upper half of the lens. What happens to the image on
A camera used by a professional photographer to shoot portraits has a focal length of 25.0 cm. The photographer takes a portrait of a person 1.50 m in front of the camera. Where is the image formed,
The lens of a certain 35 mm camera (35 mm is the width of the film strip) has a focal length of 55 mm and a speed (an f-number) of f/1.8. Determine the diameter of the lens.
A photographic image of a building is 0.092 0 m high. The image was made with a lens with a focal length of 52.0 mm. If the lens was 100 m from the building when the photograph was made, determine
The full Moon is photographed using a camera with a 120-mm-focal-length lens. Determine the diameter of the Moon’s image on the film. [Note: The radius of the Moon is 1.74 x 106 m, and the distance
A camera is being used with the correct exposure at f/4 and a shutter speed of 1/32 s. In order to “stop” a fast-moving subject, the shutter speed is changed to 1/256 s. Find the new f -stop that
(a) Use conceptual arguments to show that the intensity of light (energy per unit area per unit time) reaching the film in a camera is proportional to the square of the reciprocal of the f -number,
A certain type of film requires an exposure time of 0.010 s with an f/11 lens setting. Another type of film requires twice the light energy to produce the same level of exposure. What f -stop does
Assume that the camera in figure has a fixed focal length of 65.0 mm and is adjusted to properly focus the image of a distant object. How far and in what direction must the lens be moved to focus the
A retired bank president can easily read the fine print of the financial page when the newspaper is held no closer than arm’s length, 60.0 cm from the eye. What should be the focal length of an
A person has far points 84.4 cm from the right eye and 122 cm from the left eye. Write a prescription for the powers of the corrective lenses.
The accommodation limits for Nearsighted Nick’s eyes are 18.0 cm and 80.0 cm. When he wears his glasses, he is able to see faraway objects clearly. At what minimum distance is he able to see
The near point of an eye is 100 cm. A corrective lens is to be used to allow this eye to clearly focus on objects 25.0 in front of it. (a) What should be the focal length of the lens? (b) What is the
An individual is nearsighted; his near point is 13.0 cm and his far point is 50.0 cm. (a) What lens power is needed to correct his nearsightedness? (b) When the lenses are in use, what is this
A certain child’s near point is 10.0 cm; her far point (with eyes relaxed) is 125 cm. Each eye lens is 2.00 cm from the retina. (a) Between what limits, measured in diopters, does the power of this
An artificial lens is implanted in a person’s eye to replace a diseased lens. The distance between the artificial lens and the retina is 2.80 cm. In the absence of the lens, an image of a distant
A person is to be fitted with bifocals. She can see clearly when the object is between 30 cm and 1.5 m from the eye.(a) The upper portions of the bifocals (Figure.) should be designed to enable her
A stamp collector uses a lens with 7.5-cm focal length as a simple magnifier. The virtual image is produced at the normal near point (25 cm). (a) How far from the lens should the stamp be placed? (b)
A lens having a focal length of 25 cm is used as a simple magnifier. (a) What is the angular magnification obtained when the image is formed at the normal near point (q = – 25 cm)? (b) What is the
A biology student uses a simple magnifier to examine the structural features of the wing of an insect. The wing is held 3.50 cm in front of the lens, and the image is formed 25.0 cm from the eye. (a)
A lens that has a focal length of 5.00 cm is used as a magnifying glass. (a) To obtain maximum magnification, where should the object be placed? (b) What is the magnification?
A leaf of length h is positioned 71.0 cm in front of a converging lens with a focal length of 39.0 cm. An observer views the image of the leaf from a position 1.26 m behind the lens, as shown in
The objective lens in a microscope with a 20.0-cm-long tube has a magnification of 50.0, and the eyepiece has a magnification of 20.0. What are the focal lengths of?(a) The objective and (b) The
The desired overall magnification of a compound microscope is 140 x. The objective alone produces a lateral magnification of 12 x. Determine the required focal length of the eyepiece.
A microscope has an objective lens with a focal length of 16.22 mm and an eyepiece with a focal length of 9.50 mm. With the length of the barrel set at 29.0 cm, the diameter of a red blood cell’s
The length of a microscope tube is 15.0 cm. The focal length of the objective is 1.00 cm, and the focal length of the eyepiece is 2.50 cm. What is the magnification of the microscope, assuming it is
A certain telescope has an objective of focal length 1 500 cm. If the Moon is used as an object, a 1.0-cm-long image formed by the objective corresponds to what distance, in miles, on the Moon?
The lenses of an astronomical telescope are 92 cm apart when adjusted for viewing a distant object with minimum eyestrain. The angular magnification produced by the telescope is 45. Compute the focal
An elderly sailor is shipwrecked on a desert island, but manages to save his eyeglasses. The lens for one eye has a power of + 1.20 diopters, and the other lens has a power of + 9.00 diopters. (a)
Astronomers often take photographs with the objective lens or mirror of a telescope alone, without an eyepiece. (a) Show that the image size h’ for a telescope used in this manner is given by h’
Galileo devised a simple terrestrial telescope that produces an upright image. It consists of a converging objective lens and a diverging eyepiece at opposite ends of the telescope tube. For distant
A person decides to use an old pair of eyeglasses to make some optical instruments. He knows that the near point in his left eye is 50.0 cm and the near point in his right eye is 100 cm. (a) What is
If the distance from the Earth to the Moon is 3.8 x 108 m, what diameter would be required for a telescope objective to resolve a Moon crater 300 m in diameter? Assume a wavelength of 500 nm.
A converging lens with a diameter of 30.0 cm forms an image of a satellite passing overhead. The satellite has two green lights (wavelength 500 nm) spaced 1.00 m apart. If the lights can just be
The pupil of a cat’s eye narrows to a vertical slit of width 0.500 mm in daylight. What is the angular resolution for a pair of horizontally separated mice? (Use 500-nm light in your calculation.)
To increase the resolving power of a microscope, the object and the objective are immersed in oil (n = 1.5). If the limiting angle of resolution without the oil is 0.60 µrad, what is the limiting
(a) Calculate the limiting angle of resolution for the eye, assuming a pupil diameter of 2.00 mm, a wavelength of 500 nm in air, and an index of refraction for the eye of 1.33. (b) What is the
Two stars in a binary system are 8.0 light-years away from the observer and can just be resolved by a 20-in. telescope equipped with a filter that allows only light of wavelength 500 nm to pass. What
A spy satellite circles the Earth at an altitude of 200 km and carries out surveillance with a special high-resolution telescopic camera having a lens diameter of 35 cm. If the angular resolution of
Suppose a 5.00-m-diameter telescope were constructed on the Moon, where the absence of atmospheric distortion would permit excellent viewing. If observations were made using 500-nm light, what
The Hα line in hydrogen has a wavelength of 656.20 nm. This line differs in wavelength from the corresponding spectral line in deuterium (the heavy stable isotope of hydrogen) by 0.18 nm. (a)
A 15.0-cm-long grating has 6 000 slits per centimeter. Can two lines of wavelengths 600.000 nm and 600.003 nm be separated with this grating? Explain.
Light of wavelength 550 nm is used to calibrate a Michelson interferometer. With the use of a micrometer screw, the platform on which one mirror is mounted is moved 0.180 mm. How many fringe shifts
An interferometer is used to measure the length of a bacterium. The wavelength of the light used is 650 nm. As one arm of the interferometer is moved from one end of the cell to the other, 310 fringe
Mirror M1 in figure is displaced a distance ∆L. During this displacement, 250 fringe shifts are counted. The light being used has a wavelength of 632.8 nm. Calculate the displacement ∆L.
A thin sheet of transparent material has an index of refraction of 1.40 and is 15.0 µm thick. When it is inserted in the light path along one arm of an interferometer, how many fringe shifts occur
The Michelson interferometer can be used to measure the index of refraction of a gas by placing an evacuated transparent tube in the light path along one arm of the device. Fringe shifts occur as the
The light path in one arm of a Michelson interferometer includes a transparent cell that is 5.00 cm long. How many fringe shifts would be observed if all the air were evacuated from the cell? The
A person with a nearsighted eye has near and far points of 16 cm and 25 cm, respectively. (a) Assuming a lens is placed 2.0 cm from the eye, what power must the lens have to correct this condition?
The near point of an eye is 75.0 cm. (a) What should be the power of a corrective lens prescribed to enable the eye to see an object clearly at 25.0 cm? (b) If, using the corrective lens, the person
If a typical eyeball is 2.00 cm long and has a pupil opening that can range from about 2.00 mm to 6.00 mm, what are (a) The focal length of the eye when it is focused on objects 1.00 m away, (b) The
A cataract-impaired lens in an eye may be surgically removed and replaced by a manufactured lens. The focal length required for the new lens is determined by the lens-to-retina distance, which is
Estimate the minimum angle subtended at the eye of a hawk flying at an altitude of 50 m necessary to recognize a mouse on the ground.
The wavelengths of the sodium spectrum are λ1 = 589.00 nm and λ2 = 589.59 nm. Determine the minimum number of lines in a grating that will allow resolution of the sodium spectrum in (a) The first
The text discusses the astronomical telescope. Another type is the Galilean telescope, in which an objective lens gathers light (Figure) and tends to form an image at point A. An eyepiece consisting
A laboratory (astronomical) telescope is used to view a scale that is 300 cm from the objective, which has a focal length of 20.0 cm; the eyepiece has a focal length of 2.00 cm. Calculate the angular
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