In young's double slit experiment,the two slits are 0.5 mm apart .The screen is placed 1 m away from the slits .The distance of 11th fringe from the first fringe is 1.0 cm.Calculate the wavelength of light used.

Explanation

`d=0.5 mm = 0.5 xx 10^(-3) m`
D = 1m
`lambda = ?`
Distance of 4th dark fringe from first bright fringe `=y_(4) - y_(1) = .10 cm = 10^(-2) m`
Position of first bright fringe `= y_(m) = (mlambdaD)/d`
m =1 for first bright fringe
`y_(1) = ((1) lambda (1))/(0.5 xx 10^(-3))`
`= lambda/(0.5 xx 10^(-3)) = 2lambda xx 10^(+3)`
Position of 4th dark fringe `= y_(4) = (3+1/2) (lambda(1))/(0.5 xx 10^(-3))`
According to question
`y_(4)- y_(1) = 10^(-2)`
`5lambda xx 10^(+3) = 10^(-2)`
`lambda = 10^(-2)/(5 xx 10^(+3)) = 10^(-2)/5 xx 10^(-3)`
`lambda = 0.2 xx 10^(-5) m = 2000 m`