An isotropic point source of light is suspended h metre vertically above the centre of circular table of radius r metre. Then, the ratio of illumenances at the centre to that at the edge of the table is

Step-by-step solution

According to question, the situation is shown in the figure below E₁= I (L O)^2 = I h^2 ...(i) The illumination at the edge A is given by E₂= I (L A)^2 = I (h^2+r^2 ) ...(ii) From figure, = h (h^2+r^2 ) E₂= I h (h^2+r^2 )^ 3 / 2 Dividing Eq. (i) by Eq. (ii), we get aligned E₁ E₂ & = I / h^2 I h / (h^2+r^2 )^ 3 / 2 = (h^2+r^2 )^ 3 / 2 h^3 & = ( h^2+r^2 h^2 )^ 3 / 2 = (1+ r^2 h^2 )^ 3 / 2 aligned