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Question
A concave mirror forms a real image of an object placed in front of it at a distance 30 cm, of size three times the size of object. Find (a) the focal length of mirror (b) position of image.
Solution
u = -30 cm
m = `"I"/"O" = 30/"O" = 3`
But, for real object m is negative
∴ m = -3
∵ m = `-"v"/"u"`
∴ `-"v"/"u" = -3`
∴ v = 3u
∴ v = 3 × -30
∴ v = -90 cm
Hence, the position of the image is 90 cm in front of the mirror.
From mirror formula,
`1/"f" = 1/"v" + 1/"u"`
∴ `1/"f" = 1/(-90) + 1/(-30)`
= `-1/90 - 1/30`
= `(-1-3)/90`
= `(-4)/90`
∴ f = -22.5 cm
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