A source emits light over the range 550 to 630nm. This light is passed through a filtering system consisting of a pair of crossed polarizers between which is placed a half-wave plate constructed for light of wavelength 580nm. Explain how the crystal axis of the half-wave plate must be oriented in order to obtain maximum transmission by the filter for light of wavelength 580nm.
It is found that the system also has a maximum of transmission at 620nm. Use this information to find the thickness of the plate given that the ordinary and extraordinary refractive indeces have a mean value of 1.48 and differ by 0.7%. Any variation in refractive index with wavelength may be ignored.
Suggest how a new plate could be made to ensure transmission is achieved at only one of these wavelengths.