Question

A dentist's mirror has a radius of curvature of 3 cm. How far must it be placed from a small dental cavity to give a virtual image of the cavity that is magnified five times?

Answer 1

Given ;
Radius of curvature, R = -3 cm
Therefore, focal length, f = R/2 = -1.5 cm
magnification, m = 5
We know that, m = -v/u
=> 5 = -v/u
=> 5u = -v
=> v = -5u
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Using mirror formula we get,
1/f = (1/v)+(1/u)
(-1/1.5) = (-1/5u) + (1/u)
(-10/15) = (-1+5)/5u
-2/3 = 4/5u
-10u = 12
u = -12/10
u = -1.2 cm
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Hence the mirror should be placed 1.2 cm away from the dental cavity to produce 5 times magnification.