Two microwave coherent point sources emitting waves of wavelenths `lambda`are placed at `5lambda`distance apart.The interference is being observed on a flat non-reflecting surface along a line passing through on sources ,in a direction perpendicular to the line joining the two sources(refer figure)
Considering `lambda`as`4mn` ,calculate the positions of maxima and draw shape of interference pattern,takek initial phase differnce between the two sources to be zero.

Answer

`48,21,(32)/(9),(9)/(2),0m.m`,
`(##NG_PHY_WO_C02_E01_011_A01##)`

Explanation

Path difference at P=`S_(2)P-S_(1)P`
`=sqrt((5lambda)^(2)+x^(2))-x…(1)`
for P to be maximum
Path difference=`nlambda`…(2)from (1)&(2)and
`sqrt((5lambda)^(2)+x^(2))-x=nlambda`
`sqrt((5lambda)^(2)+x^(2))=(nlambda+x)`
`25lambda^(2)+x^(2)=n^(2)lambda^(2)+x^(2)+2nlambdax`
`(25-n^(2))lambda^(2)=2nlambdax`
`x=((25-n^(2))xxlambda)/(2n)`
`x=((25-n^(2))xx4)/(2n)mm`
for n=1,`x_(1)=48mm`
`n=2,x_(2)=21mm`
`n=3,x_(3)=(32)/(3)mm`
`n=4,x_(4)=(9)/(2)mm`
`n=5,x_(5)=0`