In the double-slit experiment of Figure below, the electric fields of the waves

Question

In the double-slit experiment of Figure below, the electric fields of the waves arriving at point P are given by the following equation, where time t is in seconds.

E1 = (2.61 ?V/m) sin[(1.47 × 1015)t]

E2 = (2.61 ?V/m) sin[(1.47 × 1015)t + 39.4 rad],

(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, in rads?

Explanation / Answer

Part a)

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 = 2.61 uV/m

phi = 39.4 rad

E = 3.44 uV/m

part b )

I = 4Iocos^2(phi/2) = 1.74 Io

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

I/Icenter = 0.435

part c)

rate = w = 1.47 x 10^15 rad/s

part d )

angle = 39.4 rad

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