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Light Reflection and Refraction
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12/08/2021 1:26 pm
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If a concave mirror has a focal length of 10 cm, find the two positions where an object can be placed to give, in each case, an image twice the height of the object.
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12/08/2021 1:31 pm
f = -10 cm
Case 1: m = 2 (Image is virtual and erect)
m = -\(\frac{v}{u}\)
2 = -\(\frac{v}{u}\)
⇒ v = -2u
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{-2u}\) + \(\frac{1}{u}\) = \(\frac{1}{-10}\)
\(\frac{1}{2u}\) = \(\frac{-1}{10}\)
u = -5 cm
Case 2: m = -2 (Image is real and inverted)
m = -\(\frac{v}{u}\)
-2 = -\(\frac{v}{u}\)
⇒ v = 2u
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{2u}\) + \(\frac{1}{u}\) = \(\frac{1}{-10}\)
\(\frac{3}{2u}\) = \(\frac{-1}{10}\)
u = -15 cm