A student is studying a book placed near the edge of a circular table of radius R. A point source of light is suspended directly above the centre of the table. What should be the height of the source above the table so as to produce maximum illuminance at the position of the book ?

Options

A. `1+(r^(2)/(h^(2)))`
B. `1+(h^(2)/(r^(2)))`
C. `{1+r^(2)/(h^(2))}^(3//2)`
D. `{1+r^(2)/(h^(2))}^(3//2)`

Answer

c

Explanation

According to question the situation is shown in the figure below

`E_(1)=(I)/((LO)^(2))=(Icostheta)/(h^(2)+r^(2))`
From figure `cos theta = (h)/(sqrt(h^(2)+R^(2))^(3)/(2)=(h^(2)+r^(2))/(h^(3))^(3)/(2)`
Dividing Eq (i) by Eq(ii) we get
`(E_(1))/(e_(2))=(I//h^(2))/(Ih//H^(2)+R^(2))^(3)/(2)=(1+(r^(2)/(H^(2)))^(3)/(2)`