Worked example - what colour does a GaAs laser emit? The band gap of GaAs is Eg = 1.42 eV. Step 1: photon energy ~ Eg, so lambda = hc/Eg. Step 2: hc = 1240 eV.nm, so lambda = 1240/1.42 = 873 nm - near-infrared, invisible to the eye (old remote controls and first CD lasers lived here). For Blu-ray's 405 nm violet: E = 1240/405 = 3.06 eV, needing a wide-gap material - gallium nitride (GaN, Eg ~ 3.4 eV). This is why short-wavelength lasers were hard: nature doesn't hand out convenient wide-gap semiconductors.