MASSACHUSETTS INSTITUTE OF TECHNOLOGY2.71 Optics Fall ’05Problem Set #6 Posted Wednesday, Oct. 26, 2005 — Due Wednesday, Nov. 2, 20051. Two plane waves of the same wavelength are propagating along the directions ofwave vectors k1, k2as shown in the figure below.1.a) Describe the interference pattern that would be observed on the plane xy.1.b) Describe the interference pattern that would be observed on a plane parallelto xy but one wavelength away towards the positive z direction.1.c) Describe the interference pattern that would be observed on the plane yz.oyxzkk301245oo30Figure. A2. A plane wave and a spherical wave, both of the same wavelength, are co-propagatingas shown in figure B on the next page.2.a) Describe the interference pattern that would be observed on a plane per-pendicular to the z axis at a distance of 1000λ away from the origin of thespherical wave.2.b) Repeat for the plane located 2000λ away from the origin of the sphericalwave.2.c) What do you observe? Explain in physical term.2.d) What is the relationship between your result and a Michelson interferometerwith a lens inserted in one of the two arms?110002000λλspherical wavekxzFigure. B3. Repeat the calculations of the previous problem for the case when the plane waveis propagating off-axis as shown in Figure C below. Explain the differences thatyou observe.o110002000λλxzspherical wave30kFigure. C4. Describe the interference pattern between two counter-propagating plane waves.This is sometimes known as a “standing wave.” Explain why.25. A “fan” of N plane waves are propagating symmetrically with respect to thez axis, as shown in figure D below. The angular spacing between successivemembers of the fan is fixed and equal to ∆θ. Describe the interference patternobserved on a plane perpendicular to the z axis.z∆θn=n=N1xFigure.
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