In an optics laboratory, a student investigates three unknown transparent solids—labeled A, B, and C—using the same monochromatic laser light in each case. The wavelength of the laser light in air is 600nm. By analyzing interference fringes produced inside each sample, the student measures the wavelength of the light within the materials and obtains
λA=450nm,λB=400nm,λC=500nm.
Air has index of refraction nair≈1.000. Neglect dispersion over the spectral width of the laser.
(a) Determine the index of refraction of each material.
(b) Rank the materials according to the speed of the photons inside them, from greatest to least. Explain your reasoning.
(c) Derive a general expression that relates a measured wavelength inside a material to the index of refraction, the wavelength in air, and any other relevant quantities.
(d) Suppose the student replaces the laser with another whose frequency is exactly twice as large. Predict qualitatively how the indices of refraction of the three materials would change, if at all, and justify your answer.