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

Explanation

(i) The distance of the `m^(th)` bright fringe from the central maximum.
`y_m = (m lamda L)/(d), y_3 = (3 lamda L)/(d) = (3 xx (6500 xx 10^(-10)) xx 1.20)/(2 xx 10^(-3))`
= 1.17mm
ii) Let the nth bright fringe of wavelength `lamda_n` and `m^th` bright fringe of wavelength a coincide at a distance `y_m` from the central maximum then
`y = (m lamda_m L)/(d) therefore m/n = (lamda_n)/(lamda_m) = 6500/5200 = 5/4`
i.e., 5th bright fringe of wavelength 5200Å coincides with the 4th bright fringe of wavelength 6500Å
` therefore y_m = (m lamda_m L)/(d) = (5(5200 xx 10^(-10)) xx 1.20)/(2 xx 10^(-3)) = 1.56mm`