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Question
An object forms a virtual image which is 1/8th of the size of the object. If the object is placed at a distance of 40 cm from the convex mirror, calculate:
- the position of the image
- the focal length of the convex mirror.
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Solution
Let size of the object = h0 = x
Size of the image h1 = `"x"/8` = + 1.25 cm
Distance of the object from the converx mirror = u = - 40 cm
Distance of the image from the convex mirror = v = ?
(i) Magnification = m = `"h"_1/"h"_0 = - "v"/"u"`
`("x"/8)/"x" = - "v"/-40`
v = `"x"/"8x" xx 40 = 5` cm
(ii) Using mirror formula:
`1/"u" + 1/"v" = 1/"f"`
We have,
`1/-40 + 1/5 = 1/"f"`
`1/"f" = - 1/40 + 1/5`
`1/"f" = (- 1 + 8)/40 = 7/40`
⇒ f = `40/7 = 5.71` cm
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