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Question:
An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.
Answer:

We have,

Object placed, distance (u) = -27 cm

A concave mirror of focal length (f) = -18 cm

 

We know, 1/f = 1/u + 1/v

or, 1/(-18) = 1/(-27) + 1/v

or, 1/v = 1/18 + 1/27

or, v = - 54 cm

Hence image formed at distance -54 cm

we know,

Magnification (m ) = - image distance (v)/ object distance(u) = Image height (h2)/ Object height (h1)

where, object height (h1) = 7 cm

Therefore,

- (54)/(-27) = Image height (h2)/7

or, Image height (h2) = - (54) x 7/(-27) =-14 cm

So, Image is formed on the same side as that of the object, since, negative sign indicated. The size of the image is 14 cm and inverted.

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