When an object is placed at a distance of 40 cm from a concave mirror, the size of image is one fourth that of the object. A. Calculate the distance of image from the mirror b. What will be the focal length of the mirror?

Explanation

Givenn u=40 cm (negative)
`m=1/4` (negative for the real image)
a. From `m=-v/u,-1/4=-v/((-40))` or v=-10 cm
Thus the image is formed at a distance 10 cm in front of the mirror.
b. Now from relation `1/u+1/v=1/f`
`1/f=1/((-40))+1/((-10))`
`=(-5)/40`
or `f=(-40)/5=-8cm`
i.e., the focal length of concave mirror is 8cm.