Question

A shopper standing 1.74 m from a convex security mirror sees his image with a magnification of 0.242. Determine the following. (Include the correct sign.)

(a) location of his image (m)

(b) focal length of the mirror (m)

(c) radius of curvature of the mirror (m)

Answer #1

Solution:

From the question we have

the distance of shopper o = 1.74 m

Magnification = M = 0.242

(a)Let us assume the image distance to be "i"

Using the formula

M = -i/o = 0.242

-i/1.74 = 0.242=> i = -0.421

Therefore, His image is at i = -0.421 m

(b)Now let f be the focal length.

Using the lens equation:

1/f = 1/i + 1/o

f = i x o / i + o = -0.421 x 1.74/ (-0.421 + 1.74) = -0.55 m

Therefore the focal length of the convex mirror = -0.55
meter.

(c)Let us consider R the radius of curvature.

As we know

R = 2 x f = 2 x -0.55 =-1.1 meters

So the radius of curvature = R = -1.1 meters.

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