At what distance an object can be placed from a convex mirror of focal length 40 cm so as to obtain image 1/5 of the size of the object?

Text Solution

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