Additional Problems 719 30. A dentist\'s mirror is placed 2.0 cm from a tooth. T

Question

Additional Problems 719 30. A dentist's mirror is placed 2.0 cm from a tooth. The when the convex side is used as a mirror, the ob enlarged image is located 5.6 cm behind the mirror. (a) What distance from the mirror? kind of mirror (plane, concave, or convex) is being used? (b) Determine the focal length of the mirror. (c) What is the magnification? (d) How is the image oriented relative to the object? 33. Consult Multiple-Concept Example 7 to see a model for solving this type of problem. A concave makeup mirror is designed so the vir- tual image it produces is twice the size of the object when the distance . 31. G A tall tree is growing across a river from you. You would between the object and the mirror is 14 cm. What is the radius of cur- like to know the distance between yourself and the tree, as well as its vature of the mirror? height, but are unable to make the measurements directly. However, *34. A concave mirror has a focal length of 30.0 cm. The distance be by using a mirror to form an image of the tree and then measuring the tween an object and its image is 45.0 cm. Find the object and image dis- image distance and the image height, you can calculate the distance tances, assuming that (a) the object lies beyond the center of curvature to the tree as well as its height. Suppose that this mirror produces an and (b) the object lies between the focal point and the mirror 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 above its surface. The speed of the spacecraft is 1620 m/s, and the image of the tree is 0.9100 m from the mirror. (a) How far away is the radius of the moon is 1.74 X 10° m. If the moon were a smooth, reflective tree? (b) The image height of the tree has a magnitude of 0.12 m. How sphere, (a) how far below the moon's surface would the image of the tall is the tree? 32, A spherical mirror is polished on both sides. When the concave side craft's image? (Hint: Both the spacecraft and its image have the same 35. ssm A spacecraft is in a circular orbit about the moon, 1.22 × 10° m spacecraft appear, and (b) what would be the apparent speed of the space- used as a mirror, the magnification is +2.0. What is the magnification angular speed about the center of the moon.) ADDITIONAL PROBLEMS WileyPLUS ·43. You walk at an angle of e-soor toward a plane mirror, as n object is placed in front of a convex mirror Draw the convex mirror (radius of curvature 15 cm) to scale, and place the object 25 cm in the drawing. Your walking velocity in front of it. Make the object height 4 cm. Using a ray diagram, locate What is the velocity of your image r the image and measure its height. Now move the object closer to the direction)? Sem Again locate its image using a ray

Explanation / Answer

32) let u and v are object and image distances when concave side is used.
let f is the focal length of the concave mirror.
we know, magnification, m = -v/u

2 = -v/u

v = -2*u

use,

1/u + 1/v = 1/f

1/u + 1/(-2*u) = 1/f

1/(2*u) = 1/f

==> u = f/2

for convex mirror, focal length is -f.

1/u + 1/v = 1/(-f)

1/(2*f) + 1/v = 1/(-f)

1/v = -1/f - 1/(2*f)

1/v = (-2 - 1)/(2*f)

1/v = -3/(2*f)

v = -2*f/(3)

so, magnification, m = -v/u

= -(-2*f/(3))/(f/2)

= 4/3 or 1.333 <<<<<<<------------------Answer

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