A plane light wave falls normally on a diaphragm with round aperature opening the first `N` Fresnel zones for a point `P` on a screen located at a distance `b` form the diaphragm. The wavelength of light is equal to `lambda`. Find the intensity of light `I_(0)` in front of the diaphragm if the distribution of intensity of light `I(r )` on the screen is knows. Here `r` is the distance from the point `P`.

Explanation

The radius of the periphery of the `N^(th)` Fresnel zone is
`r_(N) sqrt(N b lambda)`
Then by conservation of energy
`I_(0)pi (sqrt(Nb lambda)) = int_(0)^(oo) 2pi rdr I (r )`
Here `r` is the distance from the point `P`.
Thus `I_(0) = (2)/(Nb lambda) int_(0)^(oo) rdrI(r )`.