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A concave mirror has a focal length of $20 \; cm$ . At what distance from the mirror should a $4 \; cm$ tall object be placed so that it forms an image at a distance of $30 \; cm$ from the mirror ? Also calculate the size of the image formed.

Answers (1)

Concave mirror

Focal length $(f)=-20\; cm$

height of object $(h)=4\; cm$

image distance from mirror $=-30cm=v$

object distance from mirror $=u=?$

Mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{u}=\frac{1}{f}-\frac{1}{v}$

$\frac{1}{u}=\frac{1}{-20}-\frac{1}{-30}$

$\frac{1}{u}=\frac{-1}{20}+\frac{1}{30}$

$u=-60\; cm$

Magnification $m=\frac{-v}{u}$

$m=-\left [ \frac{-30}{-60} \right ]$

$m=\frac{-1}{2}$

$\frac{h_{2}}{h_{1}}=m\Rightarrow h_{2}=h_{1}\times m\Rightarrow h_{2}=4\times \left ( \frac{-1}{2} \right )$

$h_{2}=-2cm$ (size of image)

Posted by

Sumit Saini

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