Question

An object $2cm$ in size is placed $30cm$ in front of a concave mirror of focal length $15cm$. At what distance from the mirror should a screen be placed in order to obtain a sharp image? What will be the nature and the size of the image formed? Draw a ray diagram to show the formation of the image in this case.

Answer 1

$f=-15cm,h_o=2cm,u=-30cm$.

Using , $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ , we get

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{1}{-15}-\frac{1}{-30}$

$=\frac{2-1}{-30}=\frac{1}{-30}$

$\Rightarrow$ $v=-30cm$

So, screen should be placed at a distance of $30cm$ on the same side of the object in order to obtain a sharp image.

Since, $|v|=|u|=2f$, it means that the object is placed at the centre of curvature (C) of a concave mirror , the image formed is at the center of curvature , real and inverted and of the same size as the object.