A plane monochromatic light wave falls normally on a round aperture. At a distance `b = 9.0 m` from it there is a screen showing a certain diffraction pattern. The aperture diameter was decreased `eta = 3.0` times. Find the new distance `b'` at which the screen should be positioned to obtain the diffraction pattern simialer to the previous one but diminished `eta` times.

Explanation

For the radius of the periphery of the `k^(th)` zone we have
`r_(k) =sqrt(klambda(ab)/(a+b)) =sqrt(k lambdab)` if `a = oo`
If the aperture diameter is reduced `eta` times it will produce a similar deffraction pattern (reduced `eta` times) if the radii of the Fresnel zones are also `eta` times less. Thus `r'_(k) = r_(k)//eta`
This requires `b' = b//eta^(2)`.