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Question

an object of size 5cm is placed at 30cm infront of a concave mirror of focal length 20cm .At what distance should a screen be placed so that a sharp image formed on it? determine the nature and size.

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Solution

given that ;

Object size, h = + 5.0 cm;

Object distance, u = – 30.0 cm;

Focal length, f = –20 cm;

Image distance, v = ?

Image size, h′ = ?

but we have
Mirror formula is

(1/v) + (1/u) = 1/f

1/v = (1/f) − (1/u)

= (−1/20) + (1/30)

= −1/60

v = − 60 cm.

The screen should be placed at 60 cm from the mirror. The image is real.

Magnification m = h'/h = − v/u = 60/(– 30) = – 2

Height of the image h' = mh = (– 2)x5 = −10 cm

The image in inverted and enlarged.


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