Question

3. Two coherent in-phase point source, 1 and 2, of equal intensity emit outward propagating spherical waves. The sources 1 and 2 are at coordinates 3 Si=1 2 (ta ts: ©) and Sy=16 (7) respectively. The wavelength of the radiation is = 4L, Calculate the electric field and the intensity at a point P = 1(tas ta 3). fal

Answer 1

Two source given is conement, in phase and emit equal intensities. locations are S,= (o) and S₂ = 2 (-2/ Come ) Wavelength of the radiation 7=UL to comdinate of the point ( 1 ) Let light waves at si pepresented by field int 7,- qe frequency coherent in phase equal intensity light as si then As S2 emit % = a eiwt NOW, X1= and x2 = S₂ P = 5L As light froom SiP = 3L s, and se propagets to point fiel become, i(w t - Ka) Y = a e i (et- kHz) Y 2 = ae those whene k is the propag eation vector, 27 29 UL NOW, at point P total field is y=Y,+Y,

iwt 능 y = a ein -ikai -ikna te +emix) int е [ca coska, - i sinua, et cos KH₂ - isin sin ka, int a e [pria where, þ= coskait coskn2 9 = - sinka, - sinka, or y = ne a cint ✓ p²+q? -10 क tami ( ) or y A e 1 (wt-o) A = ad 6² +92 AZ I A² ar I = ? " Intensity proportonal to a² (6² +9²) (1+ 141 + 2 {coska, Cosung + sinna, sinun = 222 + 2a cosk (ag-a) 2.a? 2005 न cos (51-32)] + 2 d as a = 0 Intensity at that point is Zeroo (pestronctive interference)