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Question

At what distance from a concave mirror focal length 10 cm should an object 2 cm long be placed in order to get an erect image 6 cm tall?

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Solution

Height of the object 'ho' = 2 cm

Focal length of the mirror 'f' = −10 cm
Height of the image 'hi' = 6 cm
We have to find the d
istance of the object from the mirror 'u'.
Using the magnification formula, we get
m=hiho=-vum=62=-vum=3=-vuthus v=-3u

Now, using the mirror formula, we get

1f=1v+1u1-10=1-3u+1u110=13u-33u=-23uu=-2×103u=-6.67 cm

Thus, the distance of the object from the mirror 'u' is 6.67 cm.


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