Solved: (a) Use the thin-lens equation to derive an

When an image of a real object is formed by a flat mirror, which of the following statements are always true? (a) The image is larger than the object. (b) The image is the same size as the object. (c) The image is virtual. (d) The image is smaller than the object. (e) The image is upright.

If Joshs face is 30.0 cm in front of a concave shaving mirror creating an upright image 1.50 times as large as the object, what is the mirrors focal length? (a) 12.0 cm (b) 20.0 cm (c) 70.0 cm (d) 90.0 cm (e) none of those answers

A thin, convergent lens has a focal length of 8.00 cm. If a real, inverted image is located 12.0 cm to the right of the lens, where is the object located? (a) 12.0 cm to the left of the lens (b) 24.0 cm to the right of the lens (c) 24.0 cm to the left of the lens (d) 18.0 cm to the right of the lens (e) 18.0 cm to the left of the lens

A converging lens has a virtual object located a finite distance away. Which of the following must be true? (a) The image is virtual. (b) The image is real. (c) p , 0 (d) p . 0 (e) f . q

An object is placed 16.0 cm away from a convex mirror with a focal length of magnitude 6.00 cm. What is the location of the image? (a) 9.60 cm in front of the mirror (b) 4.36 cm in front of the mirror (c) 9.60 cm behind the mirror (d) 4.36 cm behind the mirror (e) 10.0 cm in front of the mirror

A real object is 10.0 cm to the left of a thin, diverging lens having a focal length of magnitude 16.0 cm. What is the location of the image? (a) 6.15 cm to the right of the lens (b) 6.15 cm to the left of the lens (c) 26.7 cm to the right of the lens (d) 26.7 cm to the left of the lens (e) 6.00 cm to the right of the lens

When the image of a real object is formed by a concave mirror, which of the following statements are true? (a) The image is always real. (b) The image is always virtual. (c) If the object distance is less than the focal length, the image is real. (d) If the object distance is greater than the focal length, the image is real. (e) If q , 0, the image is virtual.

An object is located 50 cm from a converging lens having a focal length of 15 cm. Which of the following is true regarding the image formed by the lens? (a) It is virtual, upright, and larger than the object. (b) It is virtual, inverted, and smaller than the object. (c) It is real, inverted, and smaller than the object. (d) It is real, inverted, and larger than the object. (e) It is real, upright, and larger than the object.

A convex mirror forms an image of a real object. Which of the following statements is always true? (a) The image is real and upright. (b) The image is virtual and larger than the object. (c) The image is virtual and upright. (d) The image is larger than the object. (e) The image is virtual and inverted.

For a real object, is the image formed by a diverging lens always (a) virtual and inverted, (b) virtual and upright, (c) real and upright, (d) real and inverted, or (e) real and magnified?

A person spearfishing from a boat sees a stationary fish a few meters away in a direction about 30 below the horizontal. To spear the fish, and assuming the spear does not change direction when it enters the water, should the person (a) aim above where he sees the fish, (b) aim below the fish, or (c) aim precisely at the fish?

An object, represented by a gray arrow, is placed in front of a plane mirror. Which of the diagrams in Figure MCQ23.12 best describes the image, represented by the pink arrow?

Why does the focal length of a mirror not depend on the mirror material when the focal length of a lens does depend on the lens material?

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 the screen? (a) Half the image would disappear. (b) The entire image would appear and remain unchanged. (c) Half the image would disappear and be dimmer. (d) The entire image would appear, but would be dimmer.

Why do some emergency vehicles have the symbol AMBULANCE written on the front?

A convex mirror has a focal length of magnitude 8.0 cm. (a) If the image is virtual, what is the object location for which the magnitude of the image distance is one third the magnitude of the object distance? (b) Find the magnification of the image and state whether it is upright or inverted.

At an intersection of hospital hallways, a convex spherical mirror is mounted high on a wall to help people avoid collisions. The magnitude of the mirrors radius of curvature is 0.550 m. (a) Locate the image of a patient located 10.0 m from the mirror. (b) Indicate whether the image is upright or inverted. (c) Determine the magnification of the image.

A concave mirror has a radius of curvature of 24.0 cm. (a) Determine the object position for which the resulting image is upright and larger than the object by a factor of 3.00. (b) Draw a ray diagram to determine the position of the image. (c) Is the image real or virtual?

A spherical mirror is to be used to form an image, five times as tall as an object, on a screen positioned 5.0 m from the mirror. (a) Describe the type of mirror required. (b) Where should the mirror be positioned relative to the object?

A ball is dropped from rest 3.00 m directly above the vertex of a concave mirror having a radius of 1.00 m and lying in a horizontal plane. (a) Describe the motion of the balls image in the mirror. (b) At what time do the ball and its image coincide?

A cubical block of ice 50.0 cm on an edge is placed on a level floor over a speck of dust. Locate the image of the speck, when viewed from directly above, if the index of refraction of ice is 1.309.

A goldfish is swimming inside a spherical bowl of water having an index of refraction n 5 1.333. Suppose the goldfish is p 5 10.0 cm from the wall of a bowl of radius uR u 5 15.0 cm, as in Figure P23.22. Neglecting the refraction of light caused by the wall of the bowl, determine the apparent distance of the goldfish from the wall according to an observer outside the bowl.

A paperweight is made of a solid glass hemisphere with index of refraction 1.50. The radius of the circular cross section is 4.0 cm. The hemisphere is placed on its flat surface, with the center directly over a 2.5-mmlong line drawn on a sheet of paper. What length of line is seen by someone looking vertically down on the hemisphere?

The top of a swimming pool is at ground level. If the pool is 2.00 m deep, how far below ground level does the bottom of the pool appear to be located when (a) the pool is completely filled with water? (b) When it is filled halfway with water?

A transparent sphere of unknown composition is observed to form an image of the Sun on its surface opposite the Sun. What is the refractive index of the sphere material?

A flint glass plate (n 5 1.66) rests on the bottom of an aquarium tank. The plate is 8.00 cm thick (vertical dimension) and covered with water (n 5 1.33) to a depth of 12.0 cm. Calculate the apparent thickness of the plate as viewed from above the water. (Assume nearly normal incidence of light rays.)

A jellyfish is floating in a water-filled aquarium 1.00 m behind a flat pane of glass 6.00 cm thick and having an index of refraction of 1.50. (a) Where is the image of the jellyfish located? (b) Repeat the problem when the glass is so thin that its thickness can be neglected. (c) How does the thickness of the glass affect the answer to part (a)?

Figure P23.28 shows a curved surface separating a material with index of refraction n1 from a material with index n2. The surface forms an image I of object O. The ray shown in red passes through the surface along a radial line. Its angles of incidence and refraction are both zero, so its direction does not change at the surface. For the ray shown in blue, the direction changes according to n1 sin u1 5 n2 sin u2. For paraxial rays, we assume u1 and u2 are small, so we may write n1 tan u1 5 n2 tan u2. The magnification is defined as M 5 h9/h. Prove that the magnification is given by M 5 2n1q/n2p.

A contact lens is made of plastic with an index of refraction of 1.50. The lens has an outer radius of curvature of 12.00 cm and an inner radius of curvature of 12.50 cm. What is the focal length of the lens?

An object is placed 50.0 cm from a screen. (a) Where should a converging lens of focal length 10.0 cm be placed to form an image on the screen? (b) Find the magnification of the lens.

A converging lens has a focal length of 10.0 cm. Locate the images for object distances of (a) 20.0 cm, (b) 10.0 cm, and (c) 5.00 cm, if they exist. For each case, state whether the image is real or virtual, upright or inverted, and find the magnification.

An object is placed 20.0 cm from a concave spherical mirror having a focal length of magnitude 40.0 cm. (a) Use graph paper to construct an accurate ray diagram for this situation. (b) From your ray diagram, determine the location of the image. (c) What is the magnification of the image? (d) Check your answers to parts (b) and (c) using the mirror equation.

A diverging lens has a focal length of magnitude 20.0 cm. (a) Locate the images for object distances of (i) 40.0 cm, (ii) 20.0 cm, and (iii) 10.0 cm. For each case, state whether the image is (b) real or virtual and (c) upright or inverted. (d) For each case, find the magnification.

A diverging lens has a focal length of 20.0 cm. Use graph paper to construct accurate ray diagrams for object distances of (a) 40.0 cm and (b) 10.0 cm. In each case determine the location of the image from the diagram and the image magnification, and state whether the image is upright or inverted. (c) Estimate the magnitude of uncertainty in locating the points in the graph. Are your answers and the uncertainty consistent with the algebraic answers found in Problem 33?

A transparent photographic slide is placed in front of a converging lens with a focal length of 2.44 cm. An image of the slide is formed 12.9 cm from the slide. How far is the lens from the slide if the image is (a) real? (b) Virtual?

The nickels image in Figure P23.36 has twice the diameter of the nickel when the lens is 2.84 cm from the nickel. Determine the focal length of the lens.

The projection lens in a certain slide projector is a single thin lens. A slide 24.0 mm high is to be projected so that its image fills a screen 1.80 m high. The slideser62060 to-screen distance is 3.00 m. (a) Determine the focal length of the projection lens. (b) How far from the slide should the lens of the projector be placed to form the image on the screen?

An object is located 20.0 cm to the left of a diverging lens having a focal length f 5 232.0 cm. Determine (a) the location and (b) the magnification of the image. (c) Construct a ray diagram for this arrangement.

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 emerges from the converging lens. Calculate the focal length of the converging lens.

(a) Use the thin-lens equation to derive an expression for q in terms of f and p. (b) Prove that for a real object and a diverging lens, the image must always be virtual. Hint: Set f 5 2u f u and show that q must be less than zero under the given conditions. (c) For a real object and converging lens, what inequality involving p and f must hold if the image is to be real?

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 magnification of the system?

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 virtual image at the position of the original object O1. (a) What is the focal length of the second lens? (b) What is the overall magnification of this system? (c) What is the nature (i.e., real or virtual, upright or inverted) of the final image?

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 216.00 cm is 6.00 cm to the right of the converging lens. Find the position and height of the final image. Is the image inverted or upright? Real or virtual?

Two converging lenses having focal lengths of f1 5 10.0 cm and f2 5 20.0 cm are placed d 5 50.0 cm apart, as shown in Figure P23.44. The final image is to be located between the lenses, at the position x 5 31.0 cm indicated. (a) How far to the left of the first lens should the object be positioned? (b) What is the overall magnification of the system? (c) Is the final image upright or inverted?

Lens L1 in Figure P23.45 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 can be varied from 5.00 cm to 10.0 cm. Determine the range of distances for which objects can be focused on the film.

An object is placed 15.0 cm from a first converging lens of focal length 10.0 cm. A second converging lens with focal length 5.00 cm is placed 10.0 cm to the right of the first converging lens. (a) Find the position q1 of the image formed by the first converging lens. (b) How far from the second lens is the image of the first lens? (c) What is the value of p2, the object position for the second lens? (d) Find the position q2 of the image formed by the second lens. (e) Calculate the magnification of the first lens. (f) Calculate the magnification of the second lens. (g) What is the total magnification for the system? (h) Is the final image real or virtual? Is it upright or inverted (compared to the original object for the lens system)?

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 image? Is the final image real or virtual?

A real objects distance from a converging lens is five times the focal length. (a) Determine the location of the image q in terms of the focal length f. (b) Find the magnification of the image. (c) Is the image real or virtual? Is it upright or inverted? Is the image on the same side of the lens as the object or on the opposite side?

The magnitudes of the radii of curvature are 32.5 cm and 42.5 cm for the two faces of a biconcave lens. The glass has index of refraction 1.53 for violet light and 1.51 for red light. For a very distant object, locate (a) the image formed by violet light and (b) the image formed by red light.

A diverging lens (n 5 1.50) is shaped like that in Active Figure 23.25c. 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. Determine the positions of the images for object distances of (b) infinity, (c) 3u f u, (d) u f u, and (e) u f u/2.

The lens and the mirror in Figure P23.51 are separated by 1.00 m and have focal lengths of 180.0 cm and 250.0 cm, respectively. If an object is placed 1.00 m to the left of the lens, where will the final image be located? State whether the image is upright or inverted, and determine the overall magnification.

The object in Figure P23.52 is midway between the lens and the mirror, which are separated by a distance d 5 25.0 cm. The magnitude of the mirrors radius of curvature is 20.0 cm, and the lens has a focal length of 216.7 cm. (a) Considering only the light that leaves the object and travels first toward the mirror, locate the final image formed by this system. (b) Is the image real or virtual? (c) Is it upright or inverted? (d) What is the overall magnification of the image?

A parallel beam of light enters a glass hemisphere perpendicular to the flat face, as shown in Figure P23.53. The radius of the hemisphere is R 5 6.00 cm, and the index of refraction is n 5 1.56. Determine the point at which the beam is focused. (Assume paraxial rays; i.e., assume all rays are located close to the principal axis.)

Two rays traveling parallel to the principal axis strike a large plano-convex lens having a refractive index of 1.60 (Fig. P23.54). If the convex face is spherical, a ray near the edge does not pass through the focal point (spherical aberration occurs). Assume this face has a radius of curvature of R 5 20.0 cm and the two rays are at distances h1 5 0.500 cm and h2 5 12.0 cm from the principal axis. Find the difference Dx in the positions where each crosses the principal axis.

To work this problem, use the fact that the image formed by the first surface becomes the object for the second surface. Figure P23.55 shows a piece of glass with index of refraction n 5 1.50 surrounded by air. The ends are hemispheres with radii R1 5 2.00 cm and R2 5 4.00 cm, and the centers of the hemispherical ends are separated by a distance of d 5 8.00 cm. A point object is in air, a distance p 5 1.00 cm from the left end of the glass. (a) Locate the image of the object due to refraction at the two spherical surfaces. (b) Is the image real or virtual?

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 P23.56. Apply the thinlens equation to each of these lenses and combine the results to show that this combination of lenses behaves like a thin lens having a focal length f given by 1/f 5 1/f1 1 1/f2. Assume the thicknesses of the lenses can be ignored in comparison to the other distances involved.

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 220.0 cm is placed 110 cm to the right of the converging lens. (a) Determine the final position and magnification of the final image. (b) Is the image upright or inverted? (c) Repeat parts (a) and (b) for the case in which the second lens is a converging lens having a focal length of 120.0 cm.

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 (Fig. P23.58). If a strawberry is placed on the bottom mirror, an image of the strawberry forms at the small opening at the center of the top mirror. Show that the final image forms at that location and describe its characteristics. Note: A flashlight beam shone on these images has a very startling effect: Even at a glancing angle, the incoming light beam is seemingly reflected off the images of the strawberry! Do you understand why?

Figure P23.59 shows a converging lens with radii R1 5 9.00 cm and R2 5 211.00 cm, in front of a concave spherical mirror of radius R 5 8.00 cm. The focal points (F1 and F2) for the thin lens and the center of curvature (C) of the mirror are also shown. (a) If the focal points F1 and F2 are 5.00 cm from the vertex of the thin lens, what is the index of refraction of the lens? (b) If the lens and mirror are 20.0 cm apart and an object is placed 8.00 cm to the left of the lens, what is the position of the final image and its magnification as seen by the eye in the figure? (c) Is the final image inverted or upright? Explain.

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 and (b) the image is virtual and the absolute value of the image distance is three times the focal length. (c) Calculate the magnification of the lens for cases (a) and (b).

The lens-makers equation for a lens with index n1 immersed in a medium with index n2 takes the form A thin diverging glass (index 5 1.50) lens with R1 5 23.00 m and R2 5 26.00 m is surrounded by air. An arrow is placed 10.0 m to the left of the lens. (a) Determine the position of the image. Repeat part (a) with the arrow and lens immersed in (b) water (index 5 1.33) (c) a medium with an index of refraction of 2.00. (d) How can a lens that is diverging in air be changed into a converging lens?

An observer to the right of the mirrorlens combination shown in Figure P23.62 sees two real images that are the same size and in the same location. One image is upright, and the other is inverted. Both images are 1.50 times larger than the object. The lens has a focal length of 10.0 cm. The lens and mirror are separated by 40.0 cm. Determine the focal length of the mirror. (Dont assume the figure is drawn to scale.)

The lens-makers 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 surrounding the lens. (a) A certain lens has focal length of 79.0 cm in air and a refractive index of 1.55. Find its focal length in water. (b) A certain mirror has focal length of 79.0 cm in air. Find its focal length in water.

A certain Christmas tree ornament is a silver sphere having a diameter of 8.50 cm. (a) If the size of an image created by reflection in the ornament is threefourths the reflected objects actual size, determine the objects location. (b) Use a principal-ray diagram to determine whether the image is upright or inverted.

A glass sphere (n 5 1.50) with a radius of 15.0 cm has a tiny air bubble 5.00 cm above its center. The sphere is viewed looking down along the extended radius containing the bubble. What is the apparent depth of the bubble below the surface of the sphere?

An object 10.0 cm tall is placed at the zero mark of a meterstick. A spherical mirror located at some point on the meterstick creates an image of the object that is upright, 4.00 cm tall, and located at the 42.0-cm mark of the meterstick. (a) Is the mirror convex or concave? (b) Where is the mirror? (c) What is the mirrors focal length?