In Young's double slit experiment the slits are separated by `0.28mm` and the screen is placed at a distance of `1.4m` away from the slits. The distance between the central bright fringe and the fifth dark fringe is measured to be `1.35cm`. Calculate the wavelength of the light used. Also find the fridge width if the screen is moved towards the slits by `0.4m`, for the same experimental set up.

Explanation

`d = 0.28mm = 0.28 times 10^(3)m`
D = 1.4m
`X_(n) = 1.35cm = 1.35 times 10^(-2)m`
n=5
For `n^(th)` dark fringe,
`x_(n)= ((2n-1)/(2)) (lamda D)/(d)`
`1.35 times 10^(-2) = [[(2 times 5)-1]]/(2) times (lamda times 1.4)/(0.28 times 10^(-3))`
`lamda = (1.35 times 10^(-2) times 0.28 times 10^(-3) times 2)/(1.4 times [(2 times 5)-1]) = 0.06 times 10^(-5) = 6000 A`
When `D = 1.4 - 0.4 = 1m`
`beta = (lamda D)/(d) = (6000 times 10^(-10) times 1)/(0.28 times 10^(-1)) = 21428.57 times 10^(-7) = 0.21cm = 2.1429 mm`