Problem 5.108

An opaque ball of diameter $D=40 \mathrm{~mm}$ is placed between a source of light with wavelength $\lambda=0.55 \mu \mathrm{m}$ and a photographic plate. The distance between the soùrce and the ball is equal to $a=12 \mathrm{~m}$ and that between the ball and the photographic plate is equal to $b=18 \mathrm{~m}$. Find: (a) the image dimension $y^{\prime}$ on the plate if the transverse dimension of the source is $y=6.0 \mathrm{~mm}$ (b) the minimum height of irregularities, covering the surface of the ball at random, at which the ball obstructs light.

Note. As calculations and experience show, that happens when the height of irregularities is comparable with the width of the Fresnel zone along which the edge of an opaque screen passes.