In the figure shown, a screen is placed normal to the line joining the two point coherent sources `S_1 and S_2`. The interference pattern consists of concentric circles.

(a)Find the radius of the nth bright ring.
(b) If d=0.5 mm, `lambda=5000 Å` and D=100 cm, find the radius of the closest second bright ring.
(c) Also, find the value of n for this ring.

Answer

A, B, C, D

Explanation

`(a) because Deltax = d cos theta`
`cos theta = 1-(theta^2)/2` (when `theta` is small)
`:. Delta x = d(1-theta^2/2)`
` =d(1-y^2/(2D^(2)))`

For nth maxima `Deltax = nlambda`
`:.` y=radius of nth bright ring.
` = Dsqrt (2(1-((nlambda)/d))). `
(b) `d = 1000 lambda`
At O, `Deltax = d = 1000lambda`
i.e. at O, 1000 th order maxima is obtained.
Substituting n=998 in,
`y=Dsqrt (2(1-((nlambda)/d)))`
We get the radius of second closest ring
r=6.32 cm
(c) n= 998