Many students when faced with studying spectra in astronomy
are force to quickly overcome any misconceptions they have
had in their understanding of light.

If students have not previously studied blackbody radiation, it
should be discussed before this activity. There is an activity on
blackbody radiation
on CSERD which shows different ways of viewing spectra.

The following points should be made:

Light occurs at many wavelengths.

Different colors of light are just light of different wavelengths.

Different types of the electromagnetic spectrum (radio, X-Ray,
etc.) are just light of different wavelengths.

Lower magnitude means higher intensity.

If a star is hotter, bigger, or closer, it will appear brighter.

If a star is cooler, smaller, or farther away, it will
appear dimmer.

Solutions

From SIMBAD: B = 2.35, V=0.58

From SIMBAD: B=0.09, V=0.12

Using the model with the above values of B and V, and modifying
the stellar temperature until the difference between the data and model
is as small as possible yields a temperature of 2940 K.

Using the model with the above values of B and V, and modifying
the stellar temperature until the difference between the data and model
is as small as possible yields a temperature of 9178 K.

Rigel has a parallax of 4.22 mas, which implies a distance of 1/(0.00422 as) =
237 parsecs.
Betelgeuse has a parallax of 7.63 mas, which implies a distance of 1/(0.00763 as) = 131 parsecs.

Using the model for Rigel with a distance of 237 parsecs, the best fit
for the model occurs (chi squared is minimized) when R=166 solar radii.
Using the model for Betelgeuse with a distance of 131 parsecs, the best fit
for the model occurs (chi squared is minimized) when R=1500 solar radii.