458 Week 13: Interference and Diffraction
Homework for Week
Problem 1.Physics Concepts
Make this week’s physics concepts summary as you work all of the problems in this week’s
assignment. Be sure to cross-reference each concept in the summary to the problem(s)
they were key to. Do the work carefully enough that you can (after it has been handed
in and graded) punch it and add it to a three ring binder for review andstudy come
finals!Problem 2.Derive the intensity as a function ofθfor the two-slit problem (where the slits are assumed
to bea≪λin width). Ford= 4λ, find the angles where the intensity is maximum and
minimum. Sketch the interference pattern fromθ∈[−π/ 2 , π/2].Problem 3.Redo problem 2, but this time assume that the slits have afinitewidth ofa= 3λand
thatd= 6λ. Determine all of the interferenceanddiffraction minima and maxima (the
latter can be approximate for diffraction) and sketch aqualitativelycorrect picture of the
interference pattern underneath the diffraction envelope.Problem 4.There are four permutations of results for thin film interference based on the relative
sizes ofn 1 ,n 2 andn 3 wheren 2 is the index of refraction of the thin film itself and
the others are the index of refraction of the first (originating medium) and third layers.
Derive the condition (relation betweentthe thickness of the film andλ 0 the wavelength
of the incident light in a vacuum) for interference maxima and minima for all four orders.
Be sure to circle on your figures the reflections at surfaces that are accompanied by a
discrete phase shift ofπ.Problem 5.Draw the phasor diagrams from which the angles at which primary andsecondary max-
ima and minima occur for five small (a≪λslits separated by a distanced. From these
diagrams write the conditions onδ=kdsinθsuch that maxima and minima occur. Find
the actual angles theta ford= 4λ, graph the intensity, and compare it to the answer to
problem 1 above.Problem 6.