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Light Reflection and Refraction
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11/08/2021 2:07 pm
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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?
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11/08/2021 2:14 pm
R = -3 cm (concave mirror)
m = 5 (virtual image)
f = \(\frac{R}{2}\) = -\(\frac{3}{2}\)
= -1.5 cm
and
m = 5 = -\(\frac{v}{u}\)
⇒ v = -5u
We have,
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{-3u}\) + \(\frac{1}{u}\) = \(\frac{1}{-15}\)
⇒ \(\frac{4}{5u}\) = -\(\frac{1}{1.5}\)
⇒ u = -\(\frac{4 \times 1.5}{5}\)
= -1.2 cm
The mirror should be placed 1.2 cm away from the dental cavity.