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 = 1` s, a slab of thickness `2 xx 10^(-3) mm` an refractive index 1.5 is placed just in front of `S_(1)`. The central maximum is formed at

Options

A. 1 mm above C
B. 1 mm below C
C. 2 mm above C
D. 2 mm below C

Answer

a

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`