The spectrum of the radiation emitted by hydrogen atoms has a peak at \(\lambda_{\mathrm{r}}=656.3 \mathrm{~nm}\) (red) and a peak at \(\lambda_{\mathrm{b}}=486.1 \mathrm{~nm}\) (blue-green).

(a) If this radiation is passed through a double-slit apparatus in which the slit separation is \(d=0.100 \mathrm{~mm}\) and is then incident on a screen placed a distance \(I .=2.10 \mathrm{~m}\) from the slits, how far apart are the \(m=1\) maxima for the two wavelengths? Can these two maxima be resolved?

(b) If, instead, a grating with 600 slits \(/ \mathrm{mm}\) is used, how far apart are the maxima now?