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Light Reflection and Refraction
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11/08/2021 1:04 pm
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An object 3 cm high is placed at a distance of 8 cm from a concave mirror which produces a virtual image 4.5 cm high:
(i) What is the focal length of the mirror?
(ii) What is the position of image?
(iii) Draw a ray-diagram to show the formation of image.
1 Answer
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11/08/2021 1:18 pm
\(h_1\) = 3 cm, u = 8 cm, \(h_2\) = 4.5 (virtual image)
(i) We know that
m = \(\frac{h_2}{h_1}\) = \(\frac{4.5}{3}\) = 1.5 and
m = \(-\frac{v}{u}\)
⇒ 1.5 = \(-\frac{v}{-8}\)
⇒ v = 1.5 x 8 = 12 cm
We have
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{12}\) + \(\frac{1}{-8}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{f}\) = \(\frac{1}{12}\) - \(\frac{1}{8}\)
= \(\frac{2 - 3}{24}\) = \(-\frac{1}{24}\)
f = -24 cm
(ii) v = 12 cm
So, the image is formed 12 cm behind the concave mirror.