A point source of light with wavelength `lambda = 0.50mu m` is located at a disatnce `a = 100cm` in front of a diaphragm with round aperture of radius `r = 1.0 mm`. Find the distance `b` between the diaphragm and the observation point for which the number of Fresnel zones in the aperture equals `k = 3`.

Explanation

By definition
`r_(k)^(2) = k(ab lambda)/(a + b)`
for the periphery of the `K^(th)` zone. Then
`ar_(k)^(2) + br_(k)^(2) = kab lambda`
So `b = (ar_(k)^(2))/(ka lambda - r_(k)^(2)) = (ar^(2))/(ka lambda - r^(2)) = 2` metre.
on putting the values.(It is given that `r = r_(k))` for `k = 3`.