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Light Reflection and Refraction
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11/08/2021 12:44 pm
Topic starter
At what distance from a concave mirror of focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall?
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11/08/2021 12:54 pm
f = 10 cm, \(h_1\) = 2 cm, \(h_2\) = 6 cm (erect image) u = ?
We know that
m = \(\frac{h_2}{h_1}\) = \(\frac{6}{2}\) = 3 and
m = \(-\frac{v}{u}\) = 3
⇒ 3u = -v
⇒ v = -3u .....(A)
We have
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{-3u}\) + \(\frac{1}{u}\) = \(\frac{1}{-10}\)
⇒ \(\frac{1}{u}\) - \(\frac{1}{3u}\) = \(-\frac{1}{10}\)
⇒ \(\frac{2}{3u}\) = \(-\frac{1}{10}\)
⇒ u = - \(\frac{20}{3}\) = - 6.66 cm
The object should be placed at a distance of 6.66 cm on the left side of the mirror.