Consider a single-slit diffraction experiment in which the amplitude of the wave
ID: 1403274 • Letter: C
Question
Consider a single-slit diffraction experiment in which the amplitude of the wave at point O in the figure 36.5a in the textbook is E0.
For each of the following cases: (a)sin?=?/2a, (b)sin?=?/a, (c) sin?=3?/2a determine the amplitude of the wave at the point question.(Hint: ?=2??asin? to determine the value of ? for each case.)
Express your answer in terms of the variables E0 and appropriate constants.
For each of the following cases: (a) sin?=?/2a, (b) sin?=?/a, (c) sin?=3?/2a compute the intensity of the wave at the point question.
Should have two answers each (Intensity and amplitude) for three different parts (a, b, and c).
Explanation / Answer
we know, amplitude
E = Eo*sin(beta/2)/(beta/2)
case a) sin(theta) = lamda/(2*a)
beta = (2*pi/lamda)*a*sin(theta)
= (2*pi/lamda)*a*(lamda/2*a)
= pi
so,
E = Eo*sin(pi/2)/(pi/2)
= 0.637*Eo
------------------------------------
case b) sin(theta) = lamda/a
beta = (2*pi/lamda)*a*sin(theta)
= (2*pi/lamda)*a*(lamda/a)
= 2*pi
so,
E = Eo*sin(2*pi/2)/(pi/2)
= 0
-----------------------------------
case c) sin(theta) = 3*lamda/2*a
beta = (2*pi/lamda)*a*sin(theta)
= (2*pi/lamda)*a*(3*lamda/2*a)
= 3*pi
so,
E = Eo*sin(3*pi/2)/(3*pi/2)
= 0.212*Eo
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comming to Intensity :
a) E^2 = (0.637*Eo)^2
I = 0.406*Io
b) I = 0
c) E^2 = (0.212*Eo)^2
= 0.045*Io