In the double-slit experiment of the figure, the electric fields of the waves ar

Question

In the double-slit experiment of the figure, the electric fields of the waves arriving at point P are given by E1 = (2.97 ?V/m) sin[(2.10 × 1015)t] E2 = (2.97 ?V/m) sin[(2.10 × 1015)t + 39.2 rad], where 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 IP at point P to the intensity Icen at the center of the interference pattern? In a phasor 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?

Explanation / Answer

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

E1 + E2 = 2Eocos(phi/2)sin(2t+phi/2)

E = 2Eocos(phi/2)

Eo = 2.97 uV/m

phi 39.2 rad

E = 4.34 uV/m

part b )

I = 4Iocos^2(phi/2) = 2.14 Io

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

I/Icenter = 0.54

part c)

rate = w = 2.10 x 10^15 rad/s

part d )

angle = 39.2 rad = 2246 degree = 86 degree

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