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 = $h_{1} = 10 c m$
Object distance = $u = - 36 c m$
Focal length = $f = - 12 c m$

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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If an object 10cm high is placed at a distance of 36 cm from a concave mirror of focal length 12cm, find the position, nature and height of image.

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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.

Given,Object size = h1=10cmObject distance = u=−36cmFocal length = f=−12cm We know that, The position of the image is 18 cm in front of the mirror. Magnification, Since image is formed left side of mirror, the image is real and inverted (since height of image is negative).