In young's double-slit experiment set up, sources S of wavelength 50 nm illumiantes two slits `S_(1)` and `S_(2)` which act as two coherent sources. The sources S oscillates about its own position according to the equation `y = 0.5 sin pi t`, where y is in nm and t in seconds. The minimum value of time t for which the intensity at point P on the screen exaclty in front of the upper slit becomes minimum is

Options

A. 1 s
B. 2 s
C. 3 s
D. 1.5 s

Answer

a

Explanation

`y ' = (d)/(2)`, at point P exactly in front of `S_(1)`
`Delta x = (y d)/(D) + (d^(2))/(2D)`
For minimum intensity, `Delta x = (2n - 1) (lambda)/(2) (n = 1)`
Putting the value, we get
`(0.5 sin pi t) xx 10^(-6) + 0.25 xx 10^(-6) = (500)/(2) xx 10^(-9)`
`0.5 sin pi t + 0.25 = (0.5)/(2)`
`sin pi t = 0 implies pi t = 0, pi, 2pi`,....
`implies t = 1 s`