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physics
light and optics

Questions and Answers of Light and Optics

Unpolarized light of intensity 20.0 W/cm2 is incident on two polarizing filters. The axis of the first filter is at an angle of 25.0° counterclockwise from the vertical (viewed in the direction the
A polarizer and an analyzer are oriented so that the maximum amount of light is transmitted. To what fraction of its maximum value is the intensity of the transmitted light reduced when the analyzer
Three Polarizing Filters three polarizing filters are stacked with the polarizing axes of the second and third at 45.0o and 90.0o, respectively, with that of the first. (a) If Unpolarized light of
Three polarizing filters are stacked, with the polarizing axis of the second and third filter at23.0o and 62.0o, respectively, to that of the first. Unpolarized light is incident on the stack the
A beam of white light passes through 8 uniform thickness of air. H the intensity of the scattered light in the middle of the green part of the visible spectrum is I, find the intensity (in terms of
Bending around Corners Traveling particles do not bend around corners, but waves do. To see why, suppose that a plane wave front strikes the edge of a sharp object traveling perpendicular to the
The Comer Reflector An inside comer of a cube is lined with mirrors to make a comer reflector (see Example 33.3 in Section 33.2). A ray of light is reflected successively from each of three mutually
A light beam is directed parallel to the axis of a hollow cylindrical tube. When the tube contains only air, it takes the light 8.72 ns to travel the length of the tube, but when the tube is filled
Light traveling in a material of refractive index n, is incident at angle θ, with respect to the normal at the interface with a slab of material that has parallel faces and refractive index n2.
In a physics lab, light with wavelength 490 nm travels in air from a laser to a photocell in 17.0ns. When a slab of glass 0.840 m thick is placed in the light beam, with the beam incident along the
A ray of light is incident in air on a block of a transparent solid whose index of refraction is n. If n = 1.38, what is the largest angle of incidence ?a for which total internal reflection will
A light ray in air strikes the right-angle prism shown in Fig. 33.46. This ray consists of two different wavelengths. When it emerges at face AB, it has been split into two different rays that
A quarter-wave plate converts linearly polarized light to circularly polarized light. Prove that a quarter-wave plate also converts circularly polarized light to linearly polarized light.
A glass plate 2.50mm thick, with an index of refraction of 1.40, is placed between a point source of light with wavelength 540 om fm vacuum) and a screen. The distance from source to screen is
Old photographic plates were made of glass with a light sensitive emulsion on the front surface. This emulsion was somewhat transparent. When a bright point source is focused on the front of the
After a long day of driving you take a late-night swim in a motel swimming pool when you go to your room you realize that you have lost your room key in the pool. You borrow a powerful flashlight and
You sight along the rim of a glass with vertical sides so that the top rim is lined up with the opposite edge of the bottom (Fig. 33.48a). The glass is a thin-walled, hollow cylinder 16.0cm high with
A beaker with a mirrored bottom is filled with a liquid whose index of refraction is 1.63. A light beam strikes the top surface of the liquid at an angle of 42.5° from the normal. At what angle from
A thin layer of ice (n = 1.309) floats on the surface of water (n = 1.333) in a bucket. A ray of light from the bottom of the bucket travels upward through the water. (a) What is the largest angle
A 45° – 45° – 90° prism is immersed in water. A ray of light is incident normally on one of its shorter faces. What is the minimum index of refraction that the prism must have if this ray is
The prism shown in Fig. 33.49 has a refractive index of 1.66, and the angles A are 25.0o. Two light rays m and n are parallel as they enter the prism. What is the angle between them after theyemerge?
Light is incident normally on the short face of a 30o ?? 60? ?? 90" prism (Fig. 33.50). A drop of liquid is placed on the hypotenuse of the prism. If the index of the prism is 1.62, find the maximum
A horizontal cylindrical tank 2.20 m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved
A large cube of glass has a metal reflector on one face and water on an adjoining face (Fig. 33.52). A light beam strikes the reflector, as shown. You observe that as you gradually increase the angle
When the sun is either rising or setting and appears to be just on the horizon, it is in fact below the horizon. The explanation for this seeming paradox is that light from the sun bends slightly
A horizontal cylindrical tank 2.20 m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved
A horizontal cylindrical tank 2.20 m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved
(c) Prove that the lateral displacement d of the emergent beam is given by the relationship where t is the thickness of the plate.(d) A ray of light is incident at an angle of 66.0o on one surface of
Light ttave1ing downward is incident on a horizontal film of thickness t, as shown in Fig. 33.57. The incident ray splits into two rays, A and B. Ray A re8ects from the top of the film. Ray B re8ects
A thin beam of white light is directed at a flat sheet of silicate flint glass at an angle of 20.0? to the surface of the sheet. Due to dispersion in the glass, the beam is spread out as shown in a
(When the light passes through symmetrically, as shown, the angle of deviation is a minimum.)(b) Use the result of part (a) to find the angle of deviation for a ray of light passing symmetrically
A beam of Unpolarized sunlight strikes the vertical plastic wall of a water tank at an unknown angle. Some of the light reflects from the wall and enters the water (Fig. 33.60). The refractive index
A beam of light traveling horizontally is made of an Unpolarized component with intensity I0 and a polarized component with intensity Ip. The plane of polarization of the polarized component is
A certain birefringent material has indexes of refraction n1, and n2 for the two perpendicular components of linearly polarized light passing through it. The corresponding wavelengths are ?, = ?0/n1,
Consider two vibrations of equal amplitude and frequency but differing in phase, one along the x-axis, x = a sin (wt - a) and the other along the y-axis, y = a sin (wt - ?) These can be written as
A rainbow is produced by the reflection of sunlight by spherical drops of water in the air. Figure 33.62 shows a ray that refracts into a drop at point A, is reflected from the back surface of the
A secondary rainbow is formed when the incident light undergoes two internal reflections in a spherical drop of water as shown in Fig. 33.20e. (a) In terms of the incident angle θAa A and the
A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where is the image formed by the mirror, and what is the height of this image?
The image of a tree just covers the length of a plane mirror 4.00 cm tall when the mirror is held 35.0 cm from the eye. The tree is 28.0 m from the mirror. What is its height?
As shown in Fig. 34.9, mirror 1 uses the image P’2 formed by mirror 2 as an object and forms an image of it. Show that this image is at point P’3, in the figure.
A concave mirror has a radius of curvature of 34.0cm.(a) What is its focal length? (b) If the mirror is immersed in water (refractive index 1.33), what is its focal length?
An object 0.600cm tall is placed 16.5cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0cm. (a) Draw a principal-ray diagram showing the formation of the
RepeatExercise34.5 for the casein which the mirror is convex
The diameter of Mars is 6794 km, and its minimum distance from the ear1h is 5.58 x 107 km. When Mars is at this distance find the diameter of the image of Mars formed by a spherical, concave,
An object is 24.0crn from the center of a silvered spherical glass Christmas tree ornament 6.00cm in diameter. What are the position and magnification of its image?
A coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 18.0 cm. An image of the 1.5-cm-tall coin is formed 6.00 cm behind the glass shell. Where is
You hold a spherical salad bowl 90cm in front of your face with the bottom of the bowl facing you. The salad bowl is made of polished metal with a 35-cm radius of curvature. (a) Where is the image of
(a) Show that Eq. (34.6) can be written as s' = sf /(s – f) and hence that the lateral magnification, given by Eq. (34.7), can be expressed as m = f / (f – s). (b) Use these formulas for s' and m
Using the formulas for s' and m obtained in part (a) of Exercise 34.11, graph s' as a function of s, and graph m as a function of s, for the case f < 0 (a convex mirror), so that f = – |f|.(a) For
Dental Mirror A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she warns an erect image with a magnification of 2.00 when the mirror is 1.25cm from a tooth (Treat
A spherical, concave, shaving mirror has a radius of curvature of 32.0cm. (a) What is the magnification of a person's face when it is 12.0cm to the left of the vertex of the mirror? (b) Where is the
A speck of dirt is embedded 3.50 cm below the surface of a sheet of ice (n = 1.309). What is its apparent depth when viewed at normal incidence?
A tank whose bottom is a mirror is filled with water to a depth of 20.0cm. A small fish floats motionless 7.0cm under the surface of the water. (a) What is the apparent depth of the fish when viewed
A Spherical Fish Bowl a small tropical fish is at the center of a water-filled, spherical fish bowl 28.0 cm in diameter.(a) Find the apparent position and magnification of the fish to an observer
The left end of a long glass rod 6.00cm in diameter has a convex hemispherical surface 3.00cm in radius. The refractive index of the glass is 1.60. Determine the position of the image if an object is
The glass rod of Exercise 34.18 is immersed in oil (n = 1.45). An object placed to the left of the rod on the rod's axis is to be imaged 1.20 m inside the rod. How far from the left end of the rod
The left end of a long glass rod 8.00cm in diameter, with an index of refraction 1.60, is ground and polished to a convex hemispherical surface with a radius of 4.00cm. An object in the form of an
Repeat Exercise 34.20 for the case in which the end of the rod is ground to a concave hemispherical surface with radius 4.00cm.
The glass rod of Exercise 34.21 is immersed in a liquid. An object 14.0 cm from the vertex of the left end of the rod and on its axis is imaged at a point 9.00cm from the vertex inside the liquid.
An insect 3.75mm tall is placed 22.5cm to the left of a thin plan convex lens. The left surface of this lens is that, the right surface has a radius of curvature of magnitude 13.0 cm, and the index
A lens forms an image of an object The object is 16.0cm from the lens. The image is 12.0cm from the lens on the same side as the object. (a) What is the focal length of the lens? Is the lens
A converging meniscus lens (see Fig. 34.32a) with a refractive index of 1.52 has spherical surfaces whose radii are 7.00cm and 4.00cm. What is the position of the image if an object is placed 24.0 cm
A converging lens with a focal length of 90.0cm forms an image of a 3.20-cm-tall real object that is to the left of the lens. The image is 4.50 cm tall and inverted. Where are the object and image
A converging lens forms an image of an 8.00-rnm-tall real object. The image is 12.0cm to the left of the lens, 3.40cm tall, and erect. What is the focal length of the lens? Where is the object
A photographic slide is to the left of a lens. The lens projects an image of the slide onto a wall 6.00 m to the right of the slide. The image is 80.0 times the size of the slide. (a) How far is the
A doub1e-convex thin lens has surfaces with equal radii of curvature of magnitude 2.50cm. Looking through this lens, you observe that it forms an image of a very distant tree at a distance of 1.87 cm
Six lenses in air are shown in Fig. 34.32. Each lens is made of a material with index of refraction n > 1. Considering each lens individually, imagine that light enters the lens from the left. Show
Exercises 34.11 and 34.12 deal with spherical mirrors(a) Show that the equations for s' and m derived in part (a) of Exercise 34.11 also apply to a thin lens. (b) A concave mirror is used in Exercise
A converging lens with a focal length of 12.0cm forms a virtual image 8.00mm tall, 17.0cm to the right of the lens. Determine the position and size of the object. Is the image erect or inverted? Are
Repeat Exercise 34.32 for the case in which the lens is diverging, with a focal length of -48.0 cm.
An object is 16.0 cm to the left of a lens. The lens forms an image 36.0cm to the right of the lens. (a) What is the focal length of the lens? Is the lens converging or diverging? (b) If the object
A camera lens has a focal length of 200 mm. How far from the lens should the subject for the photo be if the lens is 20.4cm from the film?
When a camera is focused, the lens is moved away from or toward the film. If you take a picture of your friend, who is standing 3.90 m from the lens, using a camera with a lens with a 85-mm focal
Figure 34.41 shows photographs of the same scene taken with the same camera with lenses of different focal length. If the object is 200 m from the lens, what is the magnitude of the lateral
A photographer takes a photograph of a Boeing 747 airliner Length 70.7 m) when it is flying directly overhead at an altitude of 9.50 km. The lens has a focal length of 5.00 m. How long is the image
Choosing a Camera Lens the picture size on ordinary 35-mm camera film is 24 mm x 36 mm. Focal lengths of lenses available for 35-mm cameras typically include 28, 35, 50 (the ''normal'' lens), 85,
Zoom Lens Consider the simple model of the zoom lens shown in Fig. 34.43a The converging lens has focal length f1, = 12cm, and the diverging lens has focal length f1 = - 12cm. The lenses are
A camera lens has a focal length of 180.0 mm and an aperture diameter of 16.36 mm. (a) What is the I-number of the lens?(b) If the correct exposure of a certain scene is 1/30S at f/11, what is the
Recall that the intensity of light reaching film in a camera is proportional to the effective area of the lens. Camera A has a lens with an aperture diameter of 8.00 mm. It photographs an object
Photography A 35-mm camera has a standard lens with focal length 50 mm and can focus on objects between 45 cm and infinity. (a) Is the lens for such a camera a concave or a convex lens? (b) The
You wish to project the image of a slide on a screen 9.00 m from the lens of a slide projector. (a) If the slide is placed 15.0 cm from the lens, what focal length lens is required? (b) If the
(a) Where is the near point of an eye for which a contact lens with a power of + 2.75 diopters is prescribed? (b) Where is the far point of an eye for which a contact lens with a power of -1.30
Curvature of the Cornea In a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the Exercises 1201
Corrective Lenses determine the power of the corrective contact lenses required by (a) A hyperopic eye whose near point is at 60.0 cm and (b) A myopic eye whose far point is at 60.0cm.
A thin lens with a focal length of 6.00 cm is used as a simple magnifier. (a) What angular magnification is obtainable with the lens if the object is at the focal point? (b) When an object is
The focal length of a simple magnifier is 8.00 cm. Assume the magnifier is a thin lens placed very close to the eye. (a) How far in front of the magnifier should an object be placed if the image is
You want to view an insect 2.00 mm in length through a magnifier. If the insect is to be at the focal point of the magnifier, what focal length will give the image of the insect an angular size of
You are examining an ant with a magnifying lens that has focal length 5.00 cm. If the image of the ant appears 25.0 cm from the lens, how far is the ant from the lens? On which side of the lens is
Resolution of a Microscope The image formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. The eyepiece has a focal length of 26.0 mm. (a) What is the
The focal length of the eyepiece of a certain microscope is 18.0 mm. The focal length of the objective is 8.00 mm. The distance between objective and eyepiece is 19.7 cm. The final image formed by
A certain microscope is provided with objectives that have focal lengths of 16 mm, 4 mm, and 1.9 mm and with eyepieces that have angular magnifications of 5 x and l0 X. Each objective forms an image
The Yerkes refracting telescope of the University of Chicago has an objective 1.02 m in diameter with an f-number of 19.0. (This is the largest-diameter refracting telescope in the world.) What is
The eyepiece of a refracting telescope (see Fig. 34.53) has a focal length of 9.00 cm. The distance between objective and eyepiece is 1.80 m, and the final image is at infinity. What is the angular
A telescope is constructed from two lenses with focal lengths of 95.0 cm and 15.0 cm, the 95.o.cm lens being used as the objective. Both the object being viewed and the final image are at infinity.
Saturn is viewed through the Lick Observatory refracting telescope objective focal length 18 m). If the diameter of the image of Saturn produced by the objective is 1.7 mm, what angle does Saturn
A reflecting telescope (Fig. 34.55a) is to be made by using a spherical mirror with a radius of curvature of 1.30 m and an eyepiece with a focal length of 1.10 cm. The final image is at infinity.(a)
A Cassegrain telescope is a reflecting telescope that uses two mirrors, the secondary mirror focusing the image through a hole in the primary mirror (simi1ar to that shown in Fig. 34.55b). You wish
If you run away from a plane mirror at 2.40m/s, at what speed does your image move away from you?
An object is placed between two plane mirrors arranged at right angles to each other at a distance d1 from the surface of one mirror and a distance d2 from the other. (a) How many images are formed?
What is the size of the smallest vertical plane mirror in which a woman of height h can see her full-length image?

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