Every morning Tom uses a shaving mirror with a focal length of 75 cm to view the

Question

Every morning Tom uses a shaving mirror with a focal length of 75 cm to view the image of his face. Supposing his face is 20 cm from the mirror, determine the image distance and the magnification of his face. A grocery store mounts a convex min or in the comer of the store to serve as a security minor and reduce the frequency of five-finger discounts. When you are positioned a distance of 4.8 m from the minor, your image is magnified by a factor of one-half. Determine the focal length of the minor.

Explanation / Answer

5. Shaving mirrors are concave mirrors, so the focal length f = + 75cm

object distance do = 20 cm

from the relation 1/f = 1/do + 1/di

1/di = 1/f - 1/do

therefore image distance di = f.do/( do - f)

= ( 75 x 20 ) / (20-75)

= - 27.27 cm

magnification m = - di/do  = 27.27/20 = 1.36

6. do =4.8m and m = 1/2

but m = - di/ d0

image distance di = - m.do = - 0.5 x 4.8 = - 2.4m

focal length f = ( do . di )/ (do + di)

= - 4.8 x2.4/( 4.8-2.4)

= - 4.8m

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