In a Young's double-slit experiment set up, source S of wavelength `6000 Å` illuminates two slits `S_(1)` and `S_(2)` which act two coherent sources. The sources S oscillates about its shown position according to the eqation `y = 1 + cos pi t`, where y is in millimeter and t in second.

At `t = 0`, fringe width is `beta_(1)`, and at `t = 2` s, width of figure is `beta_(2)`. Then

Options

A. `beta_(1) gt beta_(2)`
B. `beta_(2) gt beta_(1)`
C. `beta_(1) = beta_(2)`
D. data is insufficient

Answer

b

Explanation

Path difference at any point on the screen `Delta x = (bd)/(a) + (y' d)/(D)`
For central maixma. `Delta x = 0`
`implies y' = - (bd)/(a) = - ((1 + cos pi t)2)/(1)`
`y' = -2(1 + cos pi t)`
position of central maxima at any time is
`y' = - 2 (1 + "con" pi t)` mm
At `t = 2s, y,' = -4 mm`
At `t = 1` s, central maxima is at `y' = 0`.
But when a plate is inserted central maxima is at
`y_(1) = (D)/(d) (mu - 1) t = 1 mm`