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Question
A converging mirror, forms three times magnified virtual image when an object is placed at a distance of 8 cm from it. Calculate:
- the position of the image
- the focal length of the mirror.
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Solution
Let size of the object = ho = x
Size of image = h1= +3 x (Virtual image)
Distance of the object from the mirror = u = -8 cm
Distance of the image from the mirror = v = ?
Focal length of the mirror = f = ?
(i) Magnification = m = `"h"_1/"h"_0 = - "v"/"u"`
`=> "3x"/"x" = "-v"/-8`
v = 8 × 3 = 24 cm
(ii) Using mirror formula:
`1/"u" + 1/"v" = 1/"f"`
`1/-8 + 1/24 = 1/"f"`
`1/"f" = - 1/8 + 1/24`
`1/"f" = (- 3 + 1)/24 = (-2)/24 = - 1/12`
⇒ f = - 12 cm
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