Question

A real image, 1/5 th size of object is formed at a distance of 18 cm from a mirror. What is the nature of the mirror ?Calculate its focal length.

Answer 1

m = +1/5  or -1/5         and           v = +18 cm  or -18 cm

So there are 4 possibilities.   But  v positive means behind convex mirror and hence, the image has to be erect.  Hence m is positive only.  There are 3 cases only.

It is a mirror:     m = -v/u               1/f = 1/v + 1/u

case 1)

  m = +1/5  = -v/u      let v = +18 cm   

     u = - 5 v = -90 cm

    1/f = 1/18 - 1/90 = 4/90       =>  f = +22.5 cm    Convex Mirror.

case ii)

   m = +1/5 = -v/u   let  v = -18 cm

       u =  +90 cm      not possible.  as u is always negative.

case iii)

   m = -1/5 = -v/u       let v = +18 cm

        u  = +90 cm      not possible 

case iv)

    m = -1/5    = -v/u        u = 5 v

         v = -18 cm  

          1/f = -1/18 - 1/90 = -6/90

     f = -15 cm           concave mirror

hope it will help you dear!!!

Answer 2

Here the answer is

The nature of the mirror is concave