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physics
light and optics

Questions and Answers of Light and Optics

A light bulb is 4.00 m from a wall. You are to use a concave mirror to project an image of the bulb on the wall, with the image 2.25 times the size of the object. How far should the mirror be from
A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.00 m from the mirror. The filament is 6.00 mm tall, and the image is to be 36.0 cm tall. (a) How far in front of
Rear-View Mirror A mirror on the passenger side of your car is convex and has a radius of curvature with magnitude 18.0 cm. (a) Another car is seen in this side mirror and is 13.0 m behind the
Suppose the lamp filament shown in Example 34.1 (Section 34.2) is moved to a position 8.0 cm in front of the mirror.(a) Where is the image located now? Is it real or virtual? (b) What is the height
Where must you place an object in front of a concave mirror with radius R so that the image is erect and 2 ½ times the size of the object? Where is the image?
Virtual Object If the light incident from the left one a convex mirror does not diverge from an object point but instead converges toward a point at a (negative) distance. to the right of the mirror,
A layer of benzene (n = 1.50) 2.60 cm deep floats on water (n = 1.33) that is 6.50 cm deep. What is the apparent distance from the upper benzene surface to the bottom of the water layer when it is
Sketch the various possible thin lenses that can be obtained by combining two surfaces whose radii of curvature are 4.00 cm and 8.00 cm in absolute magnitude. Which are converging and which are
Figure 34.56 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is 2.0 cm along the horizontal direction, but the vertical direction is not to
You are in your car driving on a highway at 25m/s when you glance in the passenger side mirror (a convex mirror with radius of curvature 150 cm) and notice a truck approaching. If the image of the
A microscope is focused on the upper surface of a glass plate. A second plate is then placed over the first. To focus on the bottom surface of the second plate, the microscope must be raised 0.780
Three Dimensional Image The longitudinal magnification is defined as m' = ds'/ds. It relates the longitudinal dimension of a small object to the longitudinal dimension of its image. (a) Show that for
Refer to Problem 34.75. Show that the longitudinal magnification m' for refraction at a spherical surface is givenby
Pinhole Camera A pinhole camera is just a rectangular box with a tiny hole in one face. The film is on the face opposite this hole, and that is where the image is formed. The camera forms an image
A Glass Rod Both ends of a glass rod with index of refraction 1.60 are ground and polished to convex hemispherical surfaces. The radius of curvature at the left end is 6.00 cm, and the radius of
The rod in Problem 34.78 is shortened to a distance of 25.0 cm between its vertices; the curvatures of its ends remain the same. As in Problem 34.78, the object for the surface at the left end is an
Figure 34.57 shows an object and its image formed by a thin lens.(a) What is the focal length of the lens, and what type of lens (converging or diverging) is it?(b) What is the height of the image?
Figure 34.58 shows an object and its image formed by a thin lens.(a) What is the focal length of the lens, and what type of lens (converging or diverging) is it?(b) What is the height of the image?
A transparent rod 30.0 cm long is cut flat at one end and rounded to a hemispherical surface of radius 10.0 cm at the other end. A small object is embedded within the rod along its axis and halfway
A solid glass hemisphere of radius 12.0 cm and index of refraction n = 1.50 is placed with its flat face downward on a table. A parallel beam of light with a circular cross section 3.80 mm in
A thick-walled wine goblet sitting on a table can be considered to be a hollow glass sphere with an outer radius of 4.00 cm and an inner radius of 3.40 cm. The index of refraction of the goblet glass
Focus of the Eye. The cornea of the eye has a radius of curvature of approximately 0.50 cm, and the aqueous humor behind it has an index of refraction of 1.35. The thickness of the cornea itself is
A transparent rod 50.0 cm long and with a refractive index of 1.60 is cut flat at the right end and rounded to a hemispherical surface with a 15.0-cm radius at the left end. An object is placed on
What should be the index of refraction of a transparent sphere in order for paraxial rays from an infinitely distant object to be brought to a focus at the vertex of the surface opposite the point of
A glass rod with a refractive index of 1.55 is ground and polished at both ends to hemispherical surfaces with radii of 6.00 cm. When an object is placed on the axis of the rod, 25.0 cm to the left
Two thin lenses with focal lengths of magnitude 15.0 cm, the first diverging and the second converging, are placed 12.00 cm apart. An object 4.00 mm tall is placed 5.00 cm to the left of the first
The radii of curvature of the surfaces of a thin converging meniscus lens are R1 = + 12.0 cm and R2 = + 28.0 cm. The index of refraction is 1.60.(a) Compute the position and size of the image of an
An object to the left of a lens is imaged by the lens on a screen 30.0 cm to the right of the lens. When the lens is moved 4.00 cm to the right the screen must be moved 4.00 cm to the left to refocus
For refraction at a spherical surface, the first focal length f is defined as the value of s corresponding to s' = ?, as shown in Fig. 34.59a. The second focal length f' is defined as the value of s'
A convex mirror and a concave mirror are placed on the same optic axis, separated by a distance L = 0.600 m. The radius of curvature of each mirror has a magnitude of 0.360 m. A light source is
As shown in Fig. 34.61 the candle is at the center of curvature of the concave mirror, whose focal length is 10.0cm. The converging lens has a focal length of 32.0 cm and is 85.0 cm to the right of
One end of a long glass rod is ground to a convex hemispherical shape. This glass has an index of refraction of 1.55. When a small leaf is placed 20.0 cm in front of the center of the hemisphere
Two Lenses in Contact(a) Prove that when two thin lenses with focal lengths f1 and f2 are placed in contact, the focal length I of the combination is given by the relationship(b) A converging
Rays from a lens are converging toward a point image P located to the right of the lens. What thickness t of glass with index of refraction 1.60 must be interposed between the lens and P for the
A Lens in a Liquid A lens obeys Snell's law, bending light rays at each surface an amount determined by the index of refraction of the lens and the index of the medium in which the lens is
When an object is placed at the proper distance to the left of a converging lens, the image is focused on a screen 30.0cm to the right of the lens. A diverging lens is now placed 15.0cm to the right
A convex spherical mirror with a focal length of magnitude 24.0cm is placed 20.0fm to the left of a plane mirror. An object 0.250cm tall is placed midway between the surface of the plane mirror and
A glass plate 3.50cm thick, with an index of refraction of 1.55 and plane parallel faces, is held with its faces horizontal and its lower face 6.00cm above a printed page. Find the position of the
A symmetric, double-convex, thin lens made of glass with index of refraction 1.52 has a focal length in air of 40.0cm. The lens is sealed into an opening in the left-hand end of a tank filled with
You have a camera with a 35.0-mm focal length lens and 36.0-mm-wide film. You wish to take a picture of a 12.0-m-long sailboat but find that the image of the boat fills only ¼ of the width of the
An object is placed 18.0cm from a screen. (a) At what two points between object and screen may a converging lens with a 3.00-cm focal length be placed to obtain an image on the screen?(b) What is the
Three thin lenses, each with a focal length of 40.0 cm, are aligned on a common axis; adjacent lenses are separated by 52.0cm. Find the position of the image of a small object on the axis, 80.0cm to
A camera with a 90-mm-focal-Iength lens is focused on an object 130 m from the lens. To refocus on an object 6.50 m from the lens, by how much must the distance between the lens and the film be
The derivation of the expression for angular magnification, Eq. (34.22), assumed a near point of 25 cm. In fact, the near point changes with age as shown in Table 34.1. In order to achieve an angular
Angular Magnification In deriving Eq. (34.22) for the angular magnification of a magnifier, we assumed that the object is placed at the focal point of the magnifier so that the virtual image is
In one form of cataract surgery the person's natural lens, which has become cloudy, is replaced by an artificial lens. The refracting properties of the replacement lens can be chosen so that the
A Nearsighted Eye A certain very nearsighted person cannot focus on anything farther than 36.0 cm from the eye. Consider the simplified model of the eye described in Exercise 34.46. If the radius of
Focal Length of a Zoom Lens Figure 34.63 shows a simple version of a zoom lens. The converging lens has focal length f1, and the diverging lens has focal length f2 = ?? | f2|. The two lenses are
A certain reflecting telescope, constructed as shown in Fig. 34.55a, has a spherical mirror with a radius of curvature of 96.0 cm and an eyepiece with a focal length of 1.20cm. If the angular
A microscope with an objective of focal length 8.00 mm and an eyepiece of focal length 7.50 cm is used to project an image on a screen 2.00 m from the eyepiece. Let the image distance of the
The Galilean Telescope. Figure 34.64 is a diagram of a Galilean telescope, or opera glass, with both the object and its final image at infinity. The image I serve as a virtual object for the
An Object at an Angle A 16.0-cm-long pencil is placed at a 45.0? angle, with its center 15.0 cm above the optic axis and 45.0 cm from a lens with a 20.0-cm focal length as shown in Fig. 34.65. (Note
An Object at an Angle A 16.0-cm-long pencil is placed at a 45.0? angle, with its center 15.0 cm above the optic axis and 45.0 cm from a lens with a 20.0-cm focal length as shown in Fig. 34.65. (Note
(a) For a lens with focal length f, find the smallest distance possible between the object and its real image. (b) Graph the distance between the object and the real image as a function of the
Two mirrors are placed together as shown in Fig. 34.66.(a) Show that a point source in front of these mirrors and its two images lie on a circle.(b) Find the center of the circle.(c) In a diagram,
People with normal vision cannot focus their eyes underwater if they aren't wearing a face mask or goggles and there is water in contact with their eyes (see Discussion Question Q34.23).(a) Why not?
Two coherent sources A and B of radio waves are 5.00 m apart. Each source emits waves with wavelength 6.00 m. Consider points along the line between the two sources. At what distances, if any, from A
Radio Interference. Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal
A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that radiate in phase. Antenna B is 9.00nm to the right of antenna A. Consider point P between the antennas
Two light sources can be adjusted to emit monochromatic light of any visible wavelength. The two sources are coherent, 2.04µm apart, and in line with an observer, so that one source is 2.04µm
Two speakers, emitting identical sound waves of wavelength 2.0 m in phase with each other, and an observer are located as shown in Fig. 35.21.(a) At the observer's location, what is the path
Figure 35.3 shows the wave pattern produced by two identical, coherent sources emitting waves with wavelength λ and separated by a distance d = 4λ. (a) Explain why the positive y-axis
Consider Fig. 35.3, which could represent interference between water waves in a ripple tank. Pick at least three points on the anti nodal curve labeled "m = 3," and make measurements from the figure
Young's experiment is perfonned with light from excited helium atoms (λ = 502 om). Fringes are measured carefully on a screen 1.20 m away from the double slit, and the center of the 20th fringe
Two slits spaced 0.450 mm apart are placed 75.0 cm from a screen. What is the distance between the second and third dark lines of the interference pattern on the screen when the slits are illuminated
Coherent light with wavelength 450nm falls on a double slit. On a screen 1.80 m away, the distance between dark fringes is 4.20 mm. What is the separation of the slits?
Coherent light from a sodium-vapor lamp is passed through a filter that blocks everything except light of a single wavelength. It then falls on two slits separated by 0.460 mm. In the resulting
Coherent light with wavelength 400nm passes through two very narrow slits that are separated by 0.200 mm and the interference pattern is observed on a screen 4.00 m from the slits. (a) What is the
Two very narrow slits are spaced 1.80µm apart and are placed 35.0 cm from a screen. What is the distance between the first and second dark lines of the interference pattern when the slits are
Coherent light that contains two wavelengths, 660nm (red) and 470 urn (blue), passes through two narrow slits separated by 0.300 mm, and the interference pattern is observed on a screen 5.00 m from
Coherent light with wavelength 600 urn passes through two very narrow slits and the interference pattern is observed on a screen 3.00 m from the slits. The first-order bright fringe is at 4.84 mm
Coherent light of frequency 6.32 x 1014 Hz passes through two thin slits and falls on a screen 85.0 cm away. You observe that the third bright fringe occurs at ± 3.11 cm on either side of the
Two thin parallel slits that are 0.0116 mm apart are illuminated by a laser beam of wavelength 585 urn. (a) On a very large distant screen, what is the total number of bright fringes (those
An FM radio station has a frequency of 107.9 MHz and uses two identical antennas mounted at the same elevation, 12.0 m apart. The antennas radiate in phase. The resulting radiation pattern has a
In a two-slit interference pattern, the intensity at the peak ofthe central maximum is I0. (a) At a point in the pattern where the phase difference between the waves from the two slits is 60.0°,
Coherent sources A and B emit electromagnetic waves with wavelength 2.00 cm. Point P is 4.86 m from A and 5.24 m from B. What is the phase difference at P between these two waves?
Coherent light with wavelength 500nm passes through narrow slits separated by 0.340 mm. At a distance from the slits large compared to their separation, what is the phase difference (in radians) in
Coherent light with wavelength 500nm passes through narrow slits separated by 0.340 mm. At a distance from the slits large compared to their separation, what is the phase difference (in radians) in
Two slits spaced 0.260 mm apart are placed 0.700 m from a screen and illuminated by coherent light with a wavelength of 660mm. The intensity at the center of the central maximum (θ = 0o) is I0.
Show that Eq. (35.14) gives zero-intensity directions that agree with Eq. (35.5).
Points A and B are 56.0 m apart along an east-west line. At each of these points, a radio transmitter is emitting a 12.5-MHz signal horizontally. These transmitters are in phase with other and emit
Points A and B are 56.0 m apart along an east-west line. At each of these points, a radio transmitter is emitting a 12.5-MHz signal horizontally. These transmitters are in phase with other and emit
What is the thinnest film of a coating with n = 1.42 on glass (n = 1.52) for which destructive interference of the red component (650nm) of an incident white light beam in air can take place by
Non-glare Glass. When viewing a piece of art that is behind glass, one often is affected by the light that is reflected off the front of the glass (called glare), which can make it difficult to see
Two rectangular pieces of plane glass are laid one upon the other on a table. A thin strip of paper is placed between them at one edge so that a very thin wedge of air is formed. The plates are
A plate of glass 9.00cm long is placed in contact with a second plate and is held at a small angle with it by a metal strip 0.0800 mm thick placed under one end. The space between the plates is
A uniform film of TiO2, 1036nm thick and having index of refraction 2.62, is spread uniformly over the surface of crown glass of refractive index 1.52. Light of wavelength 520.0nm falls at normal
A plastic film with index of refraction 1.85 is put on the surface of a car window to increase the reflectivity and thus to keep the interior of the car cooler. The window glass has index of
The walls of a soap bubble have about the same index of refraction as that of plain water, n = 133. There is air both inside and outside the bubble. (a) What wavelength (in air) of visible light is
Light with wavelength 648nm in air is incident perpendicularly from air on a film 8.76µm thick and with refractive index 1.35. Part of the light is reflected from the first surface of the film, and
Compact Disc Player a compact disc (CD) is read from the bottom by a semiconductor laser with wavelength 790nm passing through a plastic substrate of refractive index 1.8. When the beam encounters a
What is the thinnest soap film (excluding the case of zero thickness) that appears black when illwninated with light with wavelength 480nm? The index of refraction of the film is 1.33, and there is
How far must the mirror M2 (see Fig. 35.20) of the Michel-son interferometer be moved so that 1800 fringes of He-Ne laser light (λ = 633nm) move across a line in the field of view?
Jan first uses a Michelson interferaneter with the 606-nm light from a krypton-86 lamp. He displaces the movable mirror away from him, counting 818 fringes moving across a line in his field of view.
The radius of curvature of the convex surface of a planoconvex lens is 95.2 cm. The lens is placed convex side down on a perfectly flat glass plate lhat is illuminated from above with red light
Newton's rings can be seen when a planoconvex lens is placed on a flat glass surface (see Problem 3539). For a particular lens with an index of refraction of n = 1.50 and a glass plate with an index
Suppose you illuminate two thin slits by monochromatic coherent light in air and find lhat they produce their first interference minima at ± 35.20° on either side of the central bright spot. You
A very thin sheet of brass contains two thin parallel slits. When a laser beam shines on these slits at normal incidence and room temperature (20.0oC), the first interference dark fringes occur at
Two speakers, 2.50 m apart, are driven by the same audio oscillator so that each one produces a sound consisting of two distinct frequencies, 0.900 kHz and 1.20 kHz. The speed of sound in the room is
Two radio antennas radi ating in phase are located at points A and B, 200 m apart (Fig. 35.23). The radio waves have a frequency of 5.80 MHz. A radio receiver is moved out from point B along a line

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