Miscellaneous questions (30 pts.) (a) A beam of natural light traveling in vacuum is incident normally on the surface of a fabulite slab of index of refraction 2.41. If the incident beam has an intensity of 10 W/m2 , find the intensities of the reflected and the transmitted beams. (4 points) (b) A plane wave of monochromatic light is incident normally on a uniform thin film of oil that covers a glass plate. The wavelength of the source can be varied continuously. Fully destructive interference is observed for wavelengths 500 nm and 700 nm and for no wavelengths in between. If the index of refraction of oil is 1.30 and that of glass is 1.50 find the thickness of the oil film. (6 points)