Photons are projected through a double-slit system.

(a) What must be the ratio \(d / a\) of the slit separation to slit width, so that there will be exactly nine interference maxima within the central diffraction envelope?

(b) Is any change observed on the detecting screen if the photon wavelength is changed from \(\lambda_{0}\) to \(2 \lambda_{0}\) ? If so, what?

(c) If \(10^{4}\) photons are counted within the central interference maximum, about how many do you expect will be counted within the last interference maximum that fits within the central diffraction envelope?