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Light Reflection and Refraction
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13/08/2021 2:08 pm
Topic starter
A shop security mirror 5.0 m from certain items displayed in the shop produces one-tenth magnification.
(a) What is the type of mirror?
(b) What is the radius of curvature of the mirror?
1 Answer
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13/08/2021 2:14 pm
(a) The mirror is of convex type
(b) u = -5cm, m = \(\frac{1}{10}\)
We have
m = -\(\frac{v}{u}\)
⇒ \(\frac{1}{10}\) = -\(\frac{v}{-5}\)
⇒ v = \(\frac{5}{10}\) = \(\frac{1}{2}\)m
Therefore,
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{\frac{1}{2}}\) + \(\frac{1}{-5}\) = \(\frac{1}{f}\)
\(\frac{1}{f}\) = 2 - \(\frac{1}{5}\) = \(\frac{9}{5}\)
∴ f = \(\frac{5}{9}\)m
So, radius of curvature = 2f = \(\frac{10}{9}\)m