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Question
Calculate the distance of an object of height h from a concave mirror of radius of curvature 20 cm, so as to obtain a real image of magnification 2. Find the location of the image also.
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Solution
Given: Radius of curvature of mirror = 20 cm
∴ Focal length of mirror, f = −10 cm
Since the image is real,
Magnification of image, m = −2
`m=-v/u`
`=>-2=-v/u`
`=>v=2u`
Using mirror formula,
`1/f=1/v+1/u=1/(2u)+1/u=3/(2u)`
`=>u=3/2 f=3/2xx(-10)=-15cm`
∴v=2u=−30 cm
Therefore, the distance of the object is 15 cm in front of the mirror and the position of the image is 30 cm in front of the mirror.
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