Question

The minimum size of amirror fixed on the wall of a room in which an observer at the centre of the room may see the full image on the wall of height h behind him is
a) h/3 c) 2h/3
b)h/2 d) h

Answer 1

answer is h/3

let the distance between the mirror and the observer be  X
the height above the center of mirror of the wall be = h/2

the mirror is symmetrically placed on the wall - symmetric about the center of the wall.

The wall is at 2 X  distance from the mirror.  So the image is formed at 2 X distance behind the mirror.

The size of the image will be the same as that of the object.  The size of the image above the center of mirror will be  h/2.

   Now,    (h/2) / X  = tangent of the angle of the light rays with the axis, the rays reflecting from the top of the mirror.

              Also,    (h/2 ) / (3X)  = (height of mirror) / X

             mirror height =  h /3  --- one third of size of the wall.