Two spherical concave mirrors of equal focal length are put against each other with their reflecting surfaces facing each other. The upper mirror has an opening at its centre. A small object (O) is kept at the bottom of the cavity so formed (see Figure). The top mirror produces a virtual image of the object and the lower mirror then creates a real image of the virtual image. The second image is created just outside the cavity mouth. This creates an optical illusion as if the object is raised above its original position.
(a) Prove that the height h shown in the Figure is related to focal length of the mirror as
`(1)/(f) = (1)/(h) + (1)/(h+((1)/(h)-(1)/(f))^(-1))`
(b) Rewrite the above equation in terms of `x = (h)/(f)` and solve if for x.