An object of 5.0 cm size is placed at a distance of 20.0 cm from a converging mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed to get the sharp image ? Also calculate the size of the image.

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Solution

hl=5.0cm, u=-20cm, f=-15cm, v=?, h2 = ?
We know that,
$1 over v plus 1 over u equals 1 over f fraction numerator begin display style 1 end style over denominator begin display style v end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style left parenthesis negative 20 right parenthesis end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style left parenthesis negative 15 right parenthesis end style end fraction fraction numerator begin display style 1 end style over denominator begin display style v end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 20 end style end fraction minus fraction numerator begin display style 1 end style over denominator begin display style 15 end style end fraction 1 over v equals fraction numerator negative 5 over denominator 300 end fraction v equals negative 60 c m$
The screen should be placed 60 cm in front of the mirror.

And,
$m equals h subscript i m a g e end subscript over h subscript o b j e c t end subscript equals negative v over u h subscript i m a g e end subscript over 5 equals negative fraction numerator left parenthesis negative 60 right parenthesis over denominator left parenthesis negative 20 right parenthesis end fraction h subscript i m a g e end subscript space equals space minus 15 c m$
height of image = 15cm

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Question 15
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An object of 5.0 cm size is placed at a distance of 20.0 cm from a converging mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed to get the sharp image ? Also calculate the size of the image.

hl=5.0cm, u=-20cm, f=-15cm, v=?, h2 = ? We know that, The screen should be placed 60 cm in front of the mirror. And, height of image = 15cm