Chapter 35, Problem O32 In the double-slit experiment of the figure, the electri

Question

Chapter 35, Problem O32 In the double-slit experiment of the figure, the electric fields of the waves arriving at point Pare given by E1 2.25 uv/m) si (1.72 x 10 E2 2.25 UV/m) sin (1.72 x 15 40.4 rad here time t is in seconds. (a) What is the amplitude of the resultant electric field at point P? (b) What is the ratio of the intensity lp at point P to the intensity Ican at the center of the interference pattern? In a phaso diagram of the electric fields, (c) at what rate would the phasors rotate around the origin and (d) what is the angle between the phasors? D Incident

Explanation / Answer

sin a + sin (a-b) = 2 cos ( b/2) sin ( a+ b/2)

E1+ E2 = 2 E0 cos ( phi/2) sin ( wt + phi/2)

E = 2Eo cos ( phi/2)

= 2 ( 2.25 uV/m) cos (40.4/2)

=1.41 uV/m

(b)

I = 4Iocos^2(phi/2)

I = 4Io cos^2 ( 40.4/2)

= 0.191 Io

Icenter = 4iocos^2(0) = 4Io

I/Icenter = 0.191/4 = 0.0477

(c)

Rate = 1.72 * 10^15 rad/s

(d)

the angle between phasors

phi = 40.2 rad = 2314.7494923°

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