A beam of light consisting of two wavelenths, 6500 Å and 5200 Å is used to obtain interference fringes in a Young's double slit experiment `(1 Å = 10^(-10) m).` The distance between the slits is 2.0 mm and the distance between the plane of the slits and the screen in 120 cm. (a) Find the distance of the third bright frings on the screen from the central maximum for the wavelength 6500 Å (b) What is the least distance from the central maximum where the bright frings due to both the wavlelengths coincide ?

Answer

`1.17 xx 10^(-3)m ; 15.6 xx 10^(-4)m`

Explanation

(a) `x = n lambda(D)/(d)`
`x = (3 xx (6500 xx 10^(-10)) xx 1.20)/(2 xx 10^(-3)) = 1.17 xx 10^(-3) m`
(b) If `n` is the least number of fringes of `lambda_(1) (= 6500 Å)`, which coincide with `(n + 1)` fringes of `lambda_(2) (= 5200 Å)`, then `x' = n beta = (n + 1) beta'`
`:. (n + 1)/(n) = (beta)/(beta') = (lambda_(1))/(lambda_(2))`
or `(1 + (1)/(n)) = (lambda_(1))/(lambda_(2))`
`n = (lambda_(2))/(lambda_(1) - lambda_(2)) = (5200)/(6500 - 5200) = 4`
`:. x' = n beta = n (lambda_(1)D)/(d) = (4 xx 6500 xx 10^(-10) xx 1.2)/(2 xx 10^(-3))`
`= 15.6 xx 10^(-4)m`