What is the difference between these two snowboards?

Phase Difference of Two Light Beams?

• A beam of light of wavelength 600 nm passes through two slabs of material of identical thickness d= 1.40 micrometers, as shown in the figure. The slabs have different indices of refraction: n1= 1.41 and n2= 1.58. What is the phase difference between the two parts of the beam after it passes through the slabs? I've calculated what I believe to be the difference in the number of wavelengths that fit in to each slab by applying the equation 2nt/ λ, where t is the given thickness of the slabs. The difference in question, I have calculated to be 0.793 m. My only question is how might I convert this difference into a phase difference in radians? My text gives this equation: φ = (2π/λ)*d*sinθ, but I cannot figure out how to incorperate any angle or separation distance d, because the problem does not involve slits. The beam of light simply hits two blocks of differing indices of refraction at the same time? Can anyone offer any help? It would be much appreciated!

• Answer:

  The question is defective in that it is not clearly worded. The wavelength of the light will vary according to the medium in which it travels, and we are not told what the medium is in which its wavelength is 600nm. I will answer the question as though the given wavelength refers to a vacuum, and that the required phase difference is that which exists after the 2 beams have re-emerged into vacuum again, or a the point at which they are about to do so. I will also assume that the 2 beams are in-phase when they enter the two media mentioned. Let the media be m1 & m2. Speed of light in m1 is c/n1, speed in m2 is c/n2. If d is the thickness, the difference in time required to traverse the 2 slabs is t = (d/c)*(n2 - n1) = 794*10*-18s The period (T) of the waves is L/c where L is the vacuum wavelength and c is the speed of light T = 2.00*10^-15s The phase shift in terms of number of periods is (2.00*10^-15)/794*10^-18 = 2.519 The phase difference is therefore 0.519*2*pi = 3.26rad or 2*pi - 3.26 = 3.02rad. Phase differences are usually quoted as being less than pi.