Final answer:
The etalon's maximum and minimum total reflection depend on the conditions for constructive and destructive interference related to the incident light's wavelength and the etalon's refractive index. Specific reflection coefficients can't be determined without additional details about the etalon's surface properties.
Step-by-step explanation:
The student is asking about the behavior of light interacting with an optical device known as an etalon, which is a type of interferometer used to trap light between two reflecting surfaces. In the case of an etalon with a refractive index of 2 and a thickness of 1 cm, the maximum and minimum total reflection would be determined by the conditions for constructive and destructive interference, respectively.
For destructive interference, the thickness of the etalon must be an odd multiple of the quarter-wavelength inside the medium, which is the wavelength in vacuum divided by twice the refractive index. For constructive interference, the thickness must be a multiple of the half-wavelength inside the medium. The total reflection coefficient for a wavelength of 500 nm cannot be determined without further information about the etalon's properties, such as the reflectivity and absorption of the surfaces.