What is young doubleslit experiment

Calculation of path difference Let S1 and S2 are the sources and consider a point P where we have to calculate the intensity. Path difference = S2P-S1P Using Pythagoras theorem :- (S1P) 2 = D2 + (x-(d/2)) 2 equation(1) Where D=distance of the screen from 2 slits, x= position of the point where intensity has to be found. Similarly (S2P)2 = D2+ (x+(d/2)) 2 equation(2) Where d=distance between the 2 small slits. Subtracting (2) and (1) => (S2P)2 - (S1P) 2 =(x+(d/2)) 2 - (x-(d/2)) 2 On simplifying (S2P)2 - (S1P) 2 =2xd => (S2P+S1P)(S2P- S1P)=2xd =>(S2P- S1P) =(2xd)/(S2P+S1P) If d<<D ; x<<D(screen is placed quite far away from the slit arrangement) => (S2P+S1P) (are almost same as D). => S2P+S1P =2D Therefore (S2P- S1P) = (2xd)/(2D) Path difference =(xd)/(D)Equation(2) Observation:- Light from coherent sources produced alternate dark and bright bands on the screen placed some distance