When an object is located very far away from a convex

Review Conceptual Example 2. Suppose that in Figure 25.9b the two perpendicular plane mirrors are represented by the 2x and 2y axes of an x, y coordinate system; mirror 1 is the 2x axis, and mirror 2 is the 2y axis. An object is in front of these mirrors at a point whose coordinates are x 5 22.0 m and y 5 21.0 m. Find the coordinates that locate each of the three images

On the 1y axis a laser is located at y 5 13.0 cm. The coordinates of a small target are x 5 19.0 cm and y 5 16.0 cm. The 1x axis represents the edge-on view of a plane mirror. At what point on the 1x axis should the laser be aimed in order for the laser light to hit the target after refl ection?

You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the birds image?

Suppose that you are walking perpendicularly with a velocity of 10.90 m/s toward a stationary plane mirror. What is the velocity of your image relative to you? The direction in which you walk is the positive direction

Two plane mirrors are separated by 1208, as the drawing illustrates. If a ray strikes mirror M1 at a 658 angle of incidence, at what angle u does it leave mirror M2?

The drawing shows a laser beam shining on a plane mirror that is perpendicular to the fl oor. The beams angle of incidence is 33.08. The beam emerges from the laser at a point that is 1.10 m from the mirror and 1.80 m above the fl oor. After refl ection, how far from the base of the mirror does the beam strike the fl oor?

Review Conceptual Example 1 as an aid in understanding this problem. The drawings show two arrows, A and B, that are located in front of a plane mirror. A person at point P is viewing the image of each arrow. Which images can be seen in their entirety? Determine your answers by drawing a ray from the head and foot of each arrow that refl ects from the mirror according to the law of refl ection and reaches point P. Only if both rays reach point P after refl ection can the image of that arrow be seen in its entirety

A small mirror is attached to a vertical wall, and it hangs a distance of 1.80 m above the fl oor. The mirror is facing due east, and a ray of sunlight strikes the mirror early in the morning and then again later in the morning. The incident and refl ected rays lie in a plane that is perpendicular to both the wall and the fl oor. Early in the morning, the refl ected ray strikes the fl oor at a distance of 3.86 m from the base of the wall. Later on in the morning, the ray is observed to strike the fl oor at a distance of 1.26 m from the wall. The earth rotates at a rate of 15.08 per hour. How much time (in hours) has elapsed between the two observations?

In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 50.0 km due north. A detector is placed 117 m due east of the laser. The mirror is to be aligned so that light from the laser reflects into the detector. (a) When properly aligned, what angle should the normal to the surface of the mirror make with due south? (b) Suppose the mirror is misaligned, so that the actual angle between the normal to the surface and due south is too large by 0.0048. By how many meters (due east) will the reflected ray miss the detector?

The drawing shows two plane mirrors that intersect at an angle of 508. An incident light ray refl ects from one mirror and then the other. What is the angle u between the incident and outgoing rays?

Two plane mirrors are facing each other. They are parallel, 3.00 cm apart, and 17.0 cm in length, as the drawing indicates. A laser beam is directed at the top mirror from the left edge of the bottom mirror. What is the smallest angle of incidence with respect to the top mirror, such that the laser beam (a) hits only one of the mirrors and (b) hits each mirror only once?

The drawing shows a top view of a square room. One wall is missing, and the wall on the right is a mirror. From point P in the center of the open side, a laser is pointed at the mirrored wall. At what angle of incidence must the light strike the right-hand wall so that, after being refl ected, the light hits the left corner of the back wall?

When an object is located very far away from a convex mirror, the image of the object is 18 cm behind the mirror. Using a ray diagram drawn to scale, determine where the image is located when the object is placed 9.0 cm in front of the mirror. Note that the mirror must be drawn to scale also. In your drawing, assume that the height of the object is 3.0 cm.

he image of a very distant car is located 12 cm behind a convex mirror. (a) What is the radius of curvature of the mirror? (b) Draw a ray diagram to scale showing this situation.

An object is placed 11 cm in front of a concave mirror whose focal length is 18 cm. The object is 3.0 cm tall. Using a ray diagram drawn to scale, measure (a) the location and (b) the height of the image. The mirror must be drawn to scale.

A 2.0-cm-high object is situated 15.0 cm in front of a concave mirror that has a radius of curvature of 10.0 cm. Using a ray diagram drawn to scale, measure (a) the location and (b) the height of the image. The mirror must be drawn to scale.

A convex mirror has a focal length of 240.0 cm. A 12.0-cm-tall object is located 40.0 cm in front of this mirror. Using a ray diagram drawn to scale, determine the (a) location and (b) size of the image. Note that the mirror must be drawn to scale.

A plane mirror and a concave mirror (f 5 8.0 cm) are facing each other and are separated by a distance of 20.0 cm. An object is placed between the mirrors and is 10.0 cm from each mirror. Consider the light from the object that refl ects fi rst from the plane mirror and then from the concave mirror. Using a ray diagram drawn to scale, fi nd the location of the image that this light produces in the concave mirror. Specify this distance relative to the concave mirror.

The image produced by a concave mirror is located 26 cm in front of the mirror. The focal length of the mirror is 12 cm. How far in front of the mirror is the object located?

The image behind a convex mirror (radius of curvature 5 68 cm) is located 22 cm from the mirror. (a) Where is the object located and (b) what is the magnifi cation of the mirror? Determine whether the image is (c) upright or inverted and (d) larger or smaller than the object

A concave mirror (R 5 56.0 cm) is used to project a transparent slide onto a wall. The slide is located at a distance of 31.0 cm from the mirror, and a small fl ashlight shines light through the slide and onto the mirror. The setup is similar to that in Figure 25.18a. (a) How far from the wall should the mirror be located? (b) The height of the object on the slide is 0.95 cm. What is the height of the image? (c) How should the slide be oriented, so that the picture on the wall looks normal?

A small statue has a height of 3.5 cm and is placed in front of a concave mirror. The image of the statue is inverted, 1.5 cm tall, and located 13 cm in front of the mirror. Find the focal length of the mirror.

A mirror produces an image that is located 34.0 cm behind the mirror when the object is located 7.50 cm in front of the mirror. What is the focal length of the mirror, and is the mirror concave or convex?

A concave mirror (f 5 45 cm) produces an image whose distance from the mirror is one-third the object distance. Determine (a) the object distance and (b) the (positive) image distance.

The outside mirror on the passenger side of a car is convex and has a focal length of 27.0 m. Relative to this mirror, a truck traveling in the rear has an object distance of 11 m. Find (a) the image distance of the truck and (b) the magnifi cation of the mirror.

A convex mirror has a focal length of 227.0 cm. Find the magnifi cation produced by the mirror when the object distance is 9.0 cm and 18.0 cm.

When viewed in a spherical mirror, the image of a setting sun is a virtual image. The image lies 12.0 cm behind the mirror. (a) Is the mirror concave or convex? Why? (b) What is the radius of curvature of the mirror?

A concave mirror has a focal length of 12 cm. This mirror forms an image located 36 cm in front of the mirror. What is the magnifi cation of the mirror?

An object is located 14.0 cm in front of a convex mirror, the image being 7.00 cm behind the mirror. A second object, twice as tall as the fi rst one, is placed in front of the mirror, but at a diff erent location. The image of this second object has the same height as the other image. How far in front of the mirror is the second object located?

A dentists mirror is placed 2.0 cm from a tooth. The enlarged image is located 5.6 cm behind the mirror. (a) What kind of mirror (plane, concave, or convex) is being used? (b) Determine the focal length of the mirror. (c) What is the magnifi cation? (d) How is the image oriented relative to the object?

A tall tree is growing across a river from you. You would like to know the distance between yourself and the tree, as well as its height, but are unable to make the measurements directly. However, by using a mirror to form an image of the tree and then measuring the image distance and the image height, you can calculate the distance to the tree as well as its height. Suppose that this mirror produces an image of the sun, and the image is located 0.9000 m from the mirror. The same mirror is then used to produce an image of the tree. The image of the tree is 0.9100 m from the mirror. (a) How far away is the tree? (b) The image height of the tree has a magnitude of 0.12 m. How tall is the tree?

A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnifi cation is 12.0. What is the magnifi cation * * * when the convex side is used as a mirror, the object remaining the same distance from the mirror?

Consult Multiple-Concept Example 7 to see a model for solving this type of problem. A concave makeup mirror is designed so the virtual image it produces is twice the size of the object when the distance between the object and the mirror is 14 cm. What is the radius of curvature of the mirror?

A concave mirror has a focal length of 30.0 cm. The distance between an object and its image is 45.0 cm. Find the object and image distances, assuming that (a) the object lies beyond the center of curvature and (b) the object lies between the focal point and the mirror.

A spacecraft is in a circular orbit about the moon, 1.22 3 105 m above its surface. The speed of the spacecraft is 1620 m/s, and the radius of the moon is 1.74 3 106 m. If the moon were a smooth, refl ective sphere, (a) how far below the moons surface would the image of the spacecraft appear, and (b) what would be the apparent speed of the spacecrafts image? (Hint: Both the spacecraft and its image have the same angular speed about the center of the moon.)

An object is placed in front of a convex mirror. Draw the convex mirror (radius of curvature 5 15 cm) to scale, and place the object 25 cm in front of it. Make the object height 4 cm. Using a ray diagram, locate the image and measure its height. Now move the object closer to the mirror, so the object distance is 5 cm. Again, locate its image using a ray diagram. As the object moves closer to the mirror, (a) does the magnitude of the image distance become larger or smaller, and (b) does the magnitude of the image height become larger or smaller? (c) What is the ratio of the image height when the object distance is 5 cm to its height when the object distance is 25 cm? Give your answer to one signifi cant fi gure

An object that is 25 cm in front of a convex mirror has an image located 17 cm behind the mirror. How far behind the mirror is the image located when the object is 19 cm in front of the mirror?

A concave mirror has a focal length of 42 cm. The image formed by this mirror is 97 cm in front of the mirror. What is the object distance?

Review Conceptual Example 1 before attempting this problem. A person whose eyes are 1.70 m above the fl oor stands in front of a plane mirror. The top of her head is 0.12 m above her eyes. (a) What is the height of the shortest mirror in which she can see her entire image? (b) How far above the fl oor should the bottom edge of the mirror be placed?

A drop of water on a countertop refl ects light from a fl ower held 3.0 cm directly above it. The fl owers diameter is 2.0 cm, and the diameter of the fl owers image is 0.10 cm. What is the focal length of the water drop, assuming that it may be treated as a convex spherical mirror?

A drop of water on a countertop refl ects light from a fl ower held 3.0 cm directly above it. The fl owers diameter is 2.0 cm, and the diameter of the fl owers image is 0.10 cm. What is the focal length of the water drop, assuming that it may be treated as a convex spherical mirror?

Identical objects are located at the same distance from two spherical mirrors, A and B. The magnifi cations produced by the mirrors are mA 5 4.0 and mB 5 2.0. Find the ratio fA/fB of the focal lengths of the mirrors.

You walk at an angle of u 5 50.08 toward a plane mirror, as in the drawing. Your walking velocity has a magnitude of 0.90 m/s. What is the velocity of your image relative to you (magnitude and direction)?

A candle is placed 15.0 cm in front of a convex mirror. When the convex mirror is replaced with a plane mirror, the image moves 7.0 cm farther away from the mirror. Find the focal length of the convex mirror.

An object is placed in front of a convex mirror, and the size of the image is one-fourth that of the object. What is the ratio do/f of the object distance to the focal length of the mirror?

A man holds a double-sided spherical mirror so that he is looking directly into its convex surface, 45 cm from his face. The magnifi cation of the image of his face is 10.20. What will be the image distance when he reverses the mirror (looking into its concave surface), maintaining the same distance between the mirror and his face? Be sure to include the algebraic sign (1 or 2) with your answer.

A lamp is twice as far in front of a plane mirror as a person is. Light from the lamp reaches the person via two paths, refl ected and direct. It strikes the mirror at a 30.08 angle of incidence and refl ects from it before reaching the person. The total time for the light to travel this path includes the time to travel to the mirror and the time to travel from the mirror to the person. The light also travels directly to the person without refl ecting. Find the ratio of the total travel time along the refl ected path to the travel time along the direct path

An object is located 7.0 cm in front of a mirror. The virtual image is located 4.5 cm away from the mirror and is smaller than the object. Concepts: (i) Based solely on the fact that the image is virtual, is the mirror concave or convex, or is either type possible? (ii) The image * is smaller than the object, as well as virtual. Do these characteristics together indicate a concave or convex mirror, or is either type possible? (iii) Is the focal length positive or negative? Explain. Calculation: Find the focal length of the mirror.

The radius of curvature of a mirror is 24 cm. A diamond ring is placed in front of this mirror. The image is twice the size of the ring. Concepts: (i) Is the mirror concave or convex, or is either type possible? (ii) How many places are there in front of a concave mirror where the ring can be placed and produce an image twice the size of the object? (iii) What are the possible values for the magnifi cation of the image of the ring? Calculation: Find the object distance of the ring.