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Light Reflection and Refraction
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12/08/2021 12:50 pm
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A concave mirror produces a real image 1 cm tall of an object 2.5 mm tall placed 5 cm from the mirror. Find the position of the image and the focal length of the mirror.
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12/08/2021 12:57 pm
\(h_2\) = 1 cm = 10 mm(real image), \(h_1\) = 2.5 mm, u = -5 cm = -50 mm
m = -\(\frac{h_2}{h_1}\)
m = -\(\frac{10}{2.5}\)
m = -4
And we know that
m = -\(\frac{v}{u}\)
-4 = -\(\frac{v}{-50}\)
v = -200 mm
v = -20 cm
The image is formed 20 cm in front of the mirror.
And,
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{-20}\) + \(\frac{1}{-5}\) = \(\frac{1}{f}\)
\(\frac{1}{f}\) = \(\frac{-25}{100}\)
f = -4 cm