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Light Reflection and Refraction
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11/08/2021 1:43 pm
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A concave mirror has a focal length of 4 cm and an object 2 cm tall is placed 9 cm away from it. Find the nature, position and size of the image formed.
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11/08/2021 1:50 pm
Given: \(h_1\) = 2 cm, u = 9 cm, f = 4 cm
We know that
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{v}\) = \(\frac{1}{f}\) - \(\frac{1}{u}\)
= \(\frac{1}{-4}\) - \(\frac{1}{-9}\)
= \(-\frac{1}{4}\) + \(\frac{1}{9}\)
= \(\frac{-9 + 4}{36}\) = \(-\frac{5}{36}\)
∴ v = -7.2 cm
The image is formed at a distance 7.2 cm in front of the mirror.
Again, m = \(-\frac{v}{u}\) = \(-\frac{-7.2}{-9}\) = -0.8
m = \(\frac{h_2}{h_1}\)
⇒ -0.8 = \(\frac{h_2}{2}\)
⇒ \({h_2}\) = -1.6 cm
So, Image is 1.6 cm in size, real and inverted.