One means of producing mono-energetic photons with high energy (and nearly 100 percent polarization) is through the inverse Compton effect. If an intense laser beam of 694.2 nm photons is made to collide head on with a beam of 20 GeV electrons, find (a) the energy of the incident photons in a reference frame moving with the electrons, and (b) the energy of the back-scattered photons in the laboratory reference frame. Some of the high energy photons observed in cosmic rays may have gained energy through the inverse Compton process.