In her job as a dental hygienist, Kathryn uses a concave mirror to see the back

Question

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 1.11 cm from a tooth, the image is upright and 3.02 times as large as the tooth. What are the focal length and radius of curvature of the mirror? focal length ____cm radius of curvature _____ cm

Explanation / Answer

For a concave mirror, the focal length is half the radius of curvature (a) By the magnification equation: m = -d(i)/d(o). Since the magnification is 3.02: 3.02 = -d(i)/d(o) ==> d(i) = -3.02d(o) = (-3.02)(1.11 cm) = -3.35 cm. Then, using the lens mirror equation: 1/f = 1/d(i) + 1/d(o) ==> 1/f = 1/3.35 - 1/1.11 ==> f = 1/(1/3.35 - 1/1.11) = 1.66 cm. (b) The radius of curvature is half of the focal length, so: r = f/2 = (1.66 cm)/2 = .8 cm. i hope so..... plz check out plus and minus sign..........

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