(a) In Young's double slit experiment, a monochromatic source of light S is kept equidistant from the slits `S_(1) and S_(2)`. Explain the information of dark and bright fringes on the screen.
(b) 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.
(i) Find the distance of the third bright fringe on the screen from the central maximum for wavelengths 650 nm.
(ii) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide ?
Given: The seperation between the slits is 4 mm and the distance between the screen and plane of the slits is 1.2 m.

Explanation

(b) (i) Using relation,`y = (m lambda D)/d`, where y = position of Mth bright fringe from the central bright fringe.
So ` y_(3) = (3 lambda D) / d , lambda = 650 nm, d - 4 mm, D = 1.2 m`
`rArr" "y_(3)=(3xx650xxcancel(10^(-9))_(xx1.2)^(10^(-6)))/(4 xx cancel(10^(-3)))`
` = 3 xx 65 xx 10^(-5) xx 0.3 = 40.5 xx 10^(-5)`
` = 4.05 xx 10^(-4) = 0.405 xx 10^(-3) m = 0.405 `mm
(ii) for coinciding the bright fringes, we have `y_(1) = 1//2`
` rArr" " y_(1) = (m lambda D)/d and ½ = (n lambda D)/ d `
or `(m(6 cancel 50 xx cancel10^(-9))cancelD)/cancel d=(n(5 cancel20 xx cancel10^(cancel(-9)))cancelD)/canceld`
5m = 4n
` m = 4/5 n`
`{:(n,0,1,2,3,4,5),(m,0,1.8,1.6,2.4,3.2,4):}`
4th bright fringe of 650 nm conicides with the 5th bright fringe of 520 nm.