Question

An object of size (height) $7cm$ is placed at $25cm$ in front of concave mirror of focal length $15cm$. At what distance from the mirror should a screen be placed, so that we can get a sharp and clear image? Find nature and size (height) of the image.

Answer 1

Size of object $h_o=7cm$
Size of the object $h_o=?$
Focal length $f=-15cm$
Object distance $u=-25cm$
Image distance $v=?$
Using mirror formula, $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\frac{1}{-15}=\frac{1}{v}+\frac{1}{-25}$
$\frac{1}{v}=\frac{-5+3}{75}$
$v=-37.5cm$
Hence, position of image at $37.5cm$ infront of the mirror.
Magnification(M)$=\frac{h_i}{h_o}=\frac{-v}{u}=\frac{37.5}{-25}=-1.5$
$h_i=-1.5\times h_O$
$h_i=-1.5\times 7=-10.5cm$
Hence,size of image is $-10.5cm$.
Nature of image is real,inverted and magnified.