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 = (2.26 V/m) sin[(1.97 × 1015)t]

E2 = (2.26 V/m) sin[(1.97 × 1015)t + 39.4 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?


In the double-slit experiment of the figure, the electric fields of the waves arriving at point P are given by
E1 = (2.26 V/m) sin[(1.97 × 1015)t]

E2 = (2.26 V/m) sin[(1.97 × 1015)t + 39.4 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?


In the double-slit experiment of the figure, the electric fields of the waves arriving at point P are given by
E1 = (2.26 V/m) sin[(1.97 × 1015)t]

E2 = (2.26 V/m) sin[(1.97 × 1015)t + 39.4 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? In the double-slit experiment of the figure, the electric fields of the waves arriving at point P are given by
E1 = (2.26 V/m) sin[(1.97 × 1015)t]

E2 = (2.26 V/m) sin[(1.97 × 1015)t + 39.4 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

part-a)

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

E1 + E2 = 2Eo*cos(/2)sin(2t+/2)

E = 2Eo*cos(phi/2)

Here Eo = 2.26 uV/m

= 39.4 rad

So, E = 2.98 uV/m

part b )

I = 4*Io*cos^2(phi/2)

= 1.74 Io

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

I/Icenter = 0.435

part c)

rate = = 1.97 x 10^15 rad/s

part d )

angle = 39.4 rad = 2257.5 degree

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