In figure, a screen is placed normaol to the line joining the two point coherent sources `S_(1)` and `S_(2)`. The interference pattern consists of concentric circles.

If `d = 0.5 mm, lambda = 5000 Å` and `D - 10 cm`, find the value of n for the closest second bright ring.

Options

A. 888
B. 830
C. 914
D. 998

Answer

d

Explanation

The optical path difference at P is
`Delta x = S_(1) P - S_(2) P = cos theta`
`:' cos theta = 1 - (theta^(2))/(2)` for small `theta`
`:. Delta x = d(1 - (theta^(2))/(2))`
`= d[1 - (y^(2))/(2D^(2))]`, where `D + d = D`
For nth maxima,
`implies Delta x = n lambda`
`d [1 - (y^(2))/(2D^(2))] = n lambda`
y = radius of the nth brigth ring
`= D sqrt(2(1 - (n lambda)/(d)))`
At the central maxima, `theta = 0`
`Delta x = d = n lambda`
`implies n = (d)/(lambda) = (0.5)/(0.5 xx 10^(-3)) = 1000`
Hence, for the closest second brigth ring, `n = 998`.
Putting values, `r = 6.32cm`.