Problem 2: (a) Consider the double-slit experiment in which the slit separation, d, is equal to the slit width, a. Explain how this set up is equivalent to a single-slit experiment with slit width 2a. In particular, what happens to the interference peaks of that double-slit experiment (besides the central peak)? What happens to the diffraction peaks of that double-slit experiment (besides the central peak)? Sketch the intensity pattern to elucidate the equivalence. (b) To prove that equivalence even further, show that the intensity function of the double-slit experiment [sin(/2)" (0/2) I(0) = Io cos (8/2) (1) %3D reduces to the correct intensity function of the single-slit experiment with slit width 2a. Recall o = 27 asine and 8 = 27 dsine. (c) Now ignore diffraction. A laser with 600 nanometer wavelength is shines at two slits separated by 2 millimeters. An interference pattern forms on a screen 1.5 meters behind the slits. How many maxima are illuminated on the screen? Assume the screen is very large.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Problem 2:
(a) Consider the double-slit experiment in which the slit separation, d, is equal to the slit width, a.
Explain how this set up is equivalent to a single-slit experiment with slit width 2a. In particular, what
happens to the interference peaks of that double-slit experiment (besides the central peak)? What happens
to the diffraction peaks of that double-slit experiment (besides the central peak)? Sketch the intensity
pattern to elucidate the equivalence.
(b) To prove that equivalence even further, show that the intensity function of the double-slit experiment
[sin(o/2)'
(/2)
I(0) = Io
cos (8/2)
(1)
reduces to the correct intensity function of the single-slit experiment with slit width 2a. Recall o = 27 a sine
and 8 = 27 dsin @
%3D
(c) Now ignore diffraction. A laser with 600 nanometer wavelength is shines at two slits separated by 2
millimeters. An interference pattern forms on a screen 1.5 meters behind the slits. How many maxima are
illuminated on the screen? Assume the screen is very large.
Transcribed Image Text:Problem 2: (a) Consider the double-slit experiment in which the slit separation, d, is equal to the slit width, a. Explain how this set up is equivalent to a single-slit experiment with slit width 2a. In particular, what happens to the interference peaks of that double-slit experiment (besides the central peak)? What happens to the diffraction peaks of that double-slit experiment (besides the central peak)? Sketch the intensity pattern to elucidate the equivalence. (b) To prove that equivalence even further, show that the intensity function of the double-slit experiment [sin(o/2)' (/2) I(0) = Io cos (8/2) (1) reduces to the correct intensity function of the single-slit experiment with slit width 2a. Recall o = 27 a sine and 8 = 27 dsin @ %3D (c) Now ignore diffraction. A laser with 600 nanometer wavelength is shines at two slits separated by 2 millimeters. An interference pattern forms on a screen 1.5 meters behind the slits. How many maxima are illuminated on the screen? Assume the screen is very large.
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