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In the figure below, assume that two waves of light in air, of wavelength 540 nm

ID: 1443779 • Letter: I

Question

In the figure below, assume that two waves of light in air, of wavelength 540 nm, are initially in phase. One travels through a glass layer of index of refraction n_1 = 1.70 and thickness L.The other travels through an equally thick plastic layer of index of refraction n_2= 1.45. What is the smallest value L should have if the waves are to end up with a phase difference of 5.70 rad? (b) If the waves arrive at some common point with the same amplitude, is their interference fully constructive, fully destructive, intermediate but closer to fully constructive, or intermediate but closer to fully destructive?

Explanation / Answer

path difference between them = x = n1 L - n2 L = 1.7 *L - 1.45*L = 0.25*L

phase difference = 2pi/ 540*10^-9   * 0.25L = 5.7

min L = 5.7 * 540*10^-9 /2pi*0.25 = 1959.516 nm

L = 1.96 *10^-6 m