Two coherent point sources `S_1 and S_2` emit light of wavelength `lambda`. The separation between sources is `2lambda`. Consider a line passing through `S_2` and perpendicular to the line `S_(1)S_(2)`. What is the smallest distance on this line from `S_2` where a minimum of intensity occurs?

Answer

A, B, D

Explanation

For minimum intensity
`:. S_1P-S_2P=x=(2+1)lamda/2`
Thus we get
`rarr sqrt (Z^2+(2lamda)^2)-z=(2n+1)lamda/2`
`rarr Z^2+4lamda^2(2n+1)^2lamda^2/4`
`+2Z(2n+1)lamda/2`
`rarr Z=(4lamda^2-(2n+1)2lamda^2/4)/((2n+1)lamda)`
`=(16lamda^2-(2n+1)^2lamda^2)/(4(2n+1)lamda.) `.....i
`Putting `n=0rarr z=(15lamda)/4`
`n=-1rarr z=(-15lamda)/4`
`n=1rarr z=(7lamda)/12`
`n=2rarrZ=(-9lamda)/20`
`:. Z=(7lamda)/12` is the smallest distnce for which there will be minimum intensity.