1. (15 pts) Two light beams, both of wavelength 600 nm, travel in vacuum and are
ID: 3280062 • Letter: 1
Question
1. (15 pts) Two light beams, both of wavelength 600 nm, travel in vacuum and are initially in phase. The beams each enter two thin slabs of plastic as shown in the figure below. Length L, 30.6 ,"n, L2-24.0 m, and the indices of refraction ni = 1.50 and n2-1.60. (a) What are the wavelengths of the light beams within the plastics? (b) What is the phase difference between the two beams when they emerge from the plastics? Express your answer as a fraction of wavelength . (c) After emerging from the plastics, the two beams of light reach a common point on a sereen far away. How do the rays interfere with each other? (d) Describe what, if anything, would happen to the brightness of the light on the screen if you were to rotate one of the blocks of plastic by a small amount (for instance, rotating the top block clockwise in the figure). L2 ng Continued on reverse sideExplanation / Answer
A) The wavelength coming out will be divided by the refractive index of the medium to get the changed wavelength
From 1 , 600/n1 = 600/1.5 = 400 nm
From 2 ; 600/n2 - 600/1.6 = 375 nm
B) The Phase difference is given as
Phase for wave 1; it has to travel 30600nm ,30600/400 = 76.5,
Phase for wave 2 , 24000/375 = 64
Hence wave 1 is travelling .5 wavelength more, hence the phase difference is 180 degree.
C) Waves interefere destructively at distance hence no intensity will be seen.
D) If the block is rotated clockwise the path length will increase, changing the phase difference and hence intensity will increase ,as the destrucitve interference will be no more present.(Remeber the sine curve of intensity during interference)
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