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Question
If an object of 10 cm height is placed at a distance of 36 cm from a concave mirror of focal length 12 cm, find the position, nature and height of the image.
Solution
Distance of the object from the mirror 'u' = −36 cm
Height of the object 'ho'​ = 10 cm
Focal length of the mirror 'f' = −12 cm
We have to find the distance of the image 'v'.
Height of the image hi = ?
Using the mirror formula, we get
`1/f=1/v+1/u`
`1/-12=1/v+1/(-36)`
`1/v=1/36-1/12`
`1/v=(1-3)/36=-2/36`
v=-18cm
Distance of the image 'v' = −18 cm
Using the magnification formula, we get
`m=h_i/h_o=-v/u`
`h_i/10=(-(-18))/-36=-1/2`
`h_i=-1/2`
`h_i=-1/2`
`h_i=-5cm`
Height of the image 'hi'​ = −5 cm
Again using the magnification formula, we get​
`m=-v/v=(-(-18))/36`
m=-1/2
Thus, the image is real, inverted and small in size.
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