In a modified YDSE the sources S of wavelength 5000 A oscillates about axis of setup according to the equation `y=0.5 sin(pi/6)t` where y is in millimeter and t in second. At what time ti will the intensity at P, a point exactly in front of slit `S_(1)` be maximum for the first time?

Answer

`0001`

Explanation

The path difference at point P,
`Deltax=(SS_(2)-SS_(1))+(S_(2)P-S_(1)P)`
`=(dy)/(D_(1))+(d(d//2))/D_(2)`
For constructive interference,
`Deltax=(dy)/D_(1)+d^(2)/(2D_(2))=nlambda`
`((10^(-3))(0.5sinpit)xx10^(-3))/1+(10^(-3))^(2)/(2xx2)=nlambda`
`(0.5sin(pi/6)t)xx10^(-6)+0.25xx10^(-6)`
`=(5000xx10^(-10)) n=0.5xx10^(-6)`n
`sin(pi/6)t=(0.5n-0.25)/0.5`
For the minimum value of t n=1
`sin(pi/6)t=1/2 Rightarrow (pi/6)t=pi/6 or t=1 sec`