a kid of height 1.1 ft is sleeping straight between focus and centre of curvature along the principal axis of a concave mirror of small aperture. His head is towards the mirror and is 0.5 ft from the focus of the mirror. How a plane mirror should be placed so that the image formed by it due to reflected light from the concave mirror looks Like a person of height 5.5 ft standing vertically. Draw the diagram. Find the focal length of the concave mirror.

Let focal length=fFor head, magnification m1=-f/-f-(-f-0.5) = -2f;Hence image of head is formed at v1=(-2f)(-f-0.5)...(i)Now, for feet, m2=-F/1.6=-0.635fHence image of feet is formed at v2=(-0.625f)(-f-1.6)...(ii)Hence, from (I) and (ii) we can get length of image = 1.375(f)^2This is equal to length of image formed by the plane mirror.Hence 1.375(f)^2=5.5 → f=2ft. (Ans.)And for the diagram, the plane mirror should be placed at an angle of 45° clockwise to the principal axis where image of the head is formed by convex mirror.