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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.

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Solution

Given,

Object size = h1=10cm

Object distance = u=36cm

Focal length = f=12cm

We know that,
1 over v plus 1 over u equals 1 over f fraction numerator begin display style 1 end style over denominator begin display style v end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style left parenthesis negative 36 right parenthesis end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style left parenthesis negative 12 right parenthesis end style end fraction fraction numerator begin display style 1 end style over denominator begin display style v end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 36 end style end fraction minus fraction numerator begin display style 1 end style over denominator begin display style 12 end style end fraction equals negative 2 over 36 equals negative 1 over 18 v space equals space minus 18 c m
The position of the image is 18 cm in front of the mirror.

Magnification,
m equals h subscript i m a g e end subscript over h subscript o b j e c t end subscript equals negative v over u h subscript i m a g e end subscript over 10 equals negative fraction numerator left parenthesis negative 18 right parenthesis over denominator left parenthesis negative 36 right parenthesis end fraction h subscript i m a g e end subscript equals negative 5 c m

Since image is formed left side of mirror, the image is real and inverted (since height of image is negative).


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