A laser beam of frequency 5.0×1014Hz enters perpendicularly from air into a layer of transparent oil of thickness 15cm and then into a glass block of refractive index 1.6 placed in contact with the oil. Measurements show that the wavelength of the beam inside the glass is 3.75×10−7m and that the beam takes 7.5×10−10s to cross the oil layer.
(i) Calculate the speed of light in the oil.
(ii) Determine the refractive index of the oil.
(iii) Find the wavelength of the laser beam within the oil and verify that the ratio of wavelengths in oil and glass equals the inverse ratio of their refractive indices relative to air.