A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young's double-slit experiment.
(a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.
(b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

Explanation

(a). Distance of third bright fringe from centre of screen
`x_(3)=(nDlamda)/(d)=(3xx120xx10^(-2)xx6500xx10^(-10))/(2xx10^(-3))=1.17xx10^(-3)m=1.17mm`
(b). When bright fringes coincide to each other then `n_(1)lamda_(1)=n_(2)lamda_(2)implies(n_(1))/(n_(2))=(lamda_(2))/(lamda_(1))=(5200Å)/(6500Å)=(4)/(5)`
for minimum value of `n_(1)&n_(2)" "n_(1)=4" "n_(2)=5`
So `x=(n_(1)lamda_(1)D)/(d)=(4xx6500xx10^(-10)xx120xx10^(-2))/(2xx10^(-3))=0.156xx10^(-2)m=0.156cm`