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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
- the focal length of mirror
- position of image.
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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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