Assignment 17 - Chapter 23 Problems

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course PHY 202

July 25, 2010 / 325pm

Assignment 17 - Chapter 23 ProblemsP23.1

Suppose that you want to take a photograph of yourself as you look at your image in a flat mirror 2.5m away. For what distance should the camera lens be

focused?

5.0 m...you are standing 2.5m away from the mirror and your image will appear to be 2.5m away from the surface of the mirror.

P23.2

when you look at yourself in a 60cm tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. Use ray

diagrams to show why this should be true.

P23.3

Two mirrors meet at a 135 degree angle. If light rays strike one mirror at 40 degrees, at what angle do the leave the second mirror?

The rays have an angle of incidence of 40 degrees so the angle of reflection is the same; 40 degrees. Since the two mirrors are placed at 135 degrees

to each other that means the second mirror is placed at 45 degrees to the horizontal.

The rays will leave the second mirror at 5 degrees.

P23.4

A person whose eyes are 1.68m above the floor stands 2.20m in front of a vertical plane mirror whose bottom edge is 43cm above the floor. What is the

horizontal distance to the base of the wall supporting the mirror of the nearest point on the floor that can be seen in the reflected mirror?

The angle of incidence = the angle of reflection. Setup formulas for each angle to equal each other using tan (angle).

(1.68m - 0.43m) / 2.20m = 0.43m / x -> 0.568m = 0.43m / x -> x = 0.76m

P23.7

A solar cooker, really a concave mirror pointed at the sun, focuses on the sun's rays 18.0cm in front of the mirror.

What is the radius of the spherical surfaces from which the mirror was made?

Focal length of mirror formula -> f = r/2 where f = focal length of mirror and r = radius of curvature

Rearranged this reads: r = 2f =2(18) = 36.0cm.

P23.8

How far from a concave mirror (radius 23.0cm) must an object be if its image is to be at infinity?

The focal point is the point where an object is infinitely far away.

Focal length of mirror formula -> f = r/2 where f = focal length of mirror and r = radius of curvature

f = r/2 = 23/2 = 12.5cm.

P23.11

A dentist wants a small mirror that when 2.20cm from a tooth, will produce a 4.5x upright image.

What kind of mirror must be used and what must it's radius of curvature be?

mirror equation: 1/do + 1/di = 1/f where do = object distance from ctr of mirror, di = image distance from ctr of mirror and f = r/2.

magnification equation: m = h1/ho = -di / do where do = object distance from ctr of mirror, di = image distance from ctr of mirror.

m = -di / do -> 4.5 = -di / 2.2cm -> di = (-)9.9cm

1/do + 1/di = 1/f -> 1/2.2 + 1/(-)9.9 = 1/f -> f = 2.83cm. since f = r / 2, r = 5.66cm. Dentist must use a concave mirror.

P23.14

You are standing 3.0m from a convex security mirror in a store. You estimate the height of your image to be half of you actual height.

Estimate the radius of curvature of the mirror...

mirror equation: 1/do + 1/di = 1/f where do = object distance from ctr of mirror, di = image distance from ctr of mirror and f = r/2.

magnification equation: m = h1/ho = -di / do where do = object distance from ctr of mirror, di = image distance from ctr of mirror.

m = -di / do -> 0.5 = -di / 3.0cm -> di = (-)1.5cm

1/do + 1/di = 1/f -> 1/3.0 + 1/(-)1.5 = 1/f -> f = (-)3.00cm. since f = r / 2, r = 6.00cm.

GOod, but distances are in meters, not cm.

P23.17

P23.20

The magnification of a convex mirror is +0.65x for objects 2.2m from the mirror. What is the focal length of this mirror?

m = -di / do -> 0.65 = -di / 2.2cm -> di = (-)1.43cm

1/do + 1/di = 1/f -> 1/2.2 + 1/(-)1.43 = 1/f -> f = (-)3.00cm."

again meters, not cm

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