In a Young's double slits set up, the wavelength of light used is 546nm. The distance of screen from slits is 1m. The slits separation is 0.3 mm.
(a) Compare the intensity at a point P distant 10mm from the central fringe where the intensity is `I_0`.
(b) Find the number of bright fringes between P and the central fringe.

Explanation

(a) `Deltax = (yd)/D`
and ` phi = (2pi)/lambda.Deltax`
`=((2pi)yd)/(lambdaD)`
` = ((2 xx 180)yd)/(lambdaD)` degree
` (360 xx 0.3 xx 10^-3 xx 10 xx 10^-3)/(546 xx 10^-9 xx 1.0)`
` = 1978^@`
Now, `I= I_0 "cos"^2 phi/2`
` = 2.97 xx (10^-4 I_0`
` ~~ 3.0 xx 10^-4) I_0` .
(b) `omega = (lambdaD)/d `
`:. Number of fringes between central fringe and P`
` N= y/omega = (yd)/(lambda D)`
` = ((10 xx 10^-3)(0.3 xx 10^-3))/((546 xx 10^-9)(1.0))`
= 5.49
So, bright fringes are five.