You shine light of frequency \(f_{\mathrm{i}}\) on a diffraction grating and create a diffraction pattern on a screen made up of tiny photon detectors.

(a) How does the pattern change if you increase the frequency of the light? 

\((b)\) How does the pattern change if you replace the initial light source with a source that emits brighter light of the same frequency \(f_{\mathrm{i}}\) ?

(c) For the source in part \(b\), is the number of photons detected at the screen smaller than, equal to, or greater than the number detected with the initial source?