Based on Planck's law for radiance, calculate (A) the Stefan-Boltzmann law for flux, (B) Wien's displacement law and (C) the colour index for the following ranges of two colour filters: blue: 400-500 nm; red: 600-700 nm.
Hints:
Integrate Planck's law to find the Stefan-Boltzmann law. Make substitutions to simplify the calculation.
To find Wien's displacement law, find the maximum value of Planck's law.
Use the colour-index formula, below, to find an approximate colour index for the filters listed in the problem, above.