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ID: 1492741 • Letter: F

Question

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1) In her job as a dental hygienist, Kathryn uses a concave mirror to see the back of her patient's teeth. When the mirror is 1.00 cm from a tooth, the image is upright and 2.91 times as large as the tooth. What are the focal length and radius of curvature of the mirror?

f = ____ cm

R = _____ cm

2) An object is placed in front of a convex mirror with a 27.8 cm radius of curvature. A virtual image half the size of the object is formed. At what distance is the object from the mirror?
____ cm infront/behind the mirror

Explanation / Answer

for concave mirror the focal length is positive


using 1/f = 1/do + 1/di

1/f = (1/1)+(1/di)


magnification m = -di/do = hi/ho = 2.91

di = -2.91*do = -2.91


1/f = (1/1)-(1/2.91)


focal length is f = 1.523 cm

radisu of curvature is R = 2*f= 2*1.523 = 3.046 cm


2) f = -R/2 = -27.8/2 =-13.9 cm

and hi/ho = 1/2

hi = ho/2

magnification m = -di/do = 1/2

di = -0.5*do


then using

1/f = 1/do + 1/di


(-1/13.9) = (1/do) -(1/0.5do)

do = object distance is 13.9 infront of the mirror