In the double-slit experiment of Fig. 35-10, the electric fields of the waves arriving at point P...

In the double-slit experiment of Fig. 35-10, the electric fields of the waves arriving at point P are given by

E₁ = (2.00 µV/m) sin[(1 .26 x 10¹⁵)t]

E₂ = (2.00 µV/m) sin[(1 .26 x 10¹⁵)t + 39.6 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 I_P at point P to the intensity I_cen at the center of the interference pattern? (c) Describe where point P is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies. In a phasor diagram of the electric fields, (d) at what rate would the phasors rotate around the origin and (e) what is the angle between the phasors?

Fig. 35-10 Fig. 35-10 (a) Waves from slits S₁ and S₂ (which extend into and out of the page) combine at P, an arbitrary point on screen C at distance y from the central axis. The angle θ serves as a convenient locator for P. (b) For D » d, we can approximate rays r₁ and r₂ as being parallel, at angle θ to the central axis.