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

Given `d=0.28xx10^(-3)` m , D=1.4 m
`x=1.35xx10^(-2)` m
`beta.`=? , D.=1.4-0.4 =1.0 m
For a dark fringe , path difference
`delta=(2n+1)lambda/2`
where n=0,1,2,3,4,…
Hence , `x=((2n+1)lambdaD)/(2d)`
i.e. `1.35xx10^(-2)=(((2xx4)+1)lambdaxx1.4)/(2xx0.28xx10^(-3))=lambda`
i.e. `(1.35xx0.56xx10^(-5))/12.6`
i.e. `lambda=0.06xx10^(-5)` m
or `lambda=6xx10^(-7)m` or `lambda` = 6000 A .