Question

chapter 25 question

1. Some telephoto cameras use a mirror rather than a lens. What radius of curvature mirror is needed to replace a 633.4 mm focal length telephoto lens?

2. A shopper standing 3.21 m from a convex security mirror sees his image with a magnification of 0.329. Where is his image? (Give your answer in terms of the distance in meters from the mirror.)

3. A shopper standing 2.7 m from a convex security mirror sees his image with a magnification of 0.265. What is the focal length of the mirror?

Answer 1

1-

The radius of curvature of the lens is

R=2f= 2(633.4 mm)=1266.8 mm= 1.267 m

2-

Given that,

distance of shopper = o = 3.21 meters (He is actually object in this case, that is why denoted as "o")

Magnification = M = 0.329

We need to find the image distance. Let it be "i"

We know that,

M = -i/o = 0.329

-i/3.21 = 0.329 => i = -1.0561

Hence, His image is at i = -1.0561 m

3-

distance of shopper = o = 2.7 meters (He is actually object in this case, that is why denoted as "o")

Magnification = M = 0.265

We need to find the image distance. Let it be "i"

We know that,

M = -i/o = 0.265

-i/2.7 = 0.265 => i = -0.7155 m

Let f be the focal length. We know that from lens equation:

1/f = 1/i + 1/o

f = i x o / i + o = -0.7155 x 2.7 / (-0.7155 + 2.7)

= -0.97 m

Hence, the focal length of the convex mirror = -0.97 meter.

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