Problem $33\mathrm{.}31$

Your artist friend is designing an exhibit inspired by circular$-$aperture diffraction. A pinhole in a red zone is going to be illuminated with a red laser beam of wavelength $670$ nm $,$ while a pinhole in a violet zone is going to be illuminated with a violet laser beam of wavelength $410$ nm $.$ She wants all the diffraction patterns seen on a distant screen to have the same size.