Question

A convex mirror form an image one -fourth the size of object . If object at a distance 0.5m from the mirror ,the focal length of the mirror Is

Answer 1

firstly find value of v by linear magnification then use mirror formula

Answer 2

The focal length is 0.16 m

SOLUTION:

The mirror given is a convex mirror

Let object height be “h” , so  

$h_{o}=h$

The question states that the size of image is one-fourth to that of object.

So height of image is $h_{v}=\frac{h}{4}$

According to the magnification formula

$\frac{h_{v}}{h_{e}}=-\frac{v}{u}$

The object is placed at position of 0.5 m , so  

u = 0.5 m

Putting value in the magnification formula  

We have,

$\frac{h}{4 h}=-\frac{v}{-0.5}$

So the image position is v = 0.125 m

Using mirror formula to detect the focal length

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

$\frac{1}{f}=\frac{1}{0.125}+\frac{1}{-0.5}$

$\frac{1}{f}=6$

So, the focal length is $f=\frac{1}{6}=0.16 m$