In Young's double-slit experiment, the slit are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slits, It is found that the ninth bright fringe is at a distance of 7.5 mm from the second dark fringe from the center of the fringe pattern. The wavelength of the light used is

Answer

`5000Å`

Explanation

`beta=(lambdaD)/(d)`
Position of `9^(th)` bright fringe=`9beta`
Position of `2^(nd)` dark fringe=`(3beta)/(2)`
distance between `9^('th)` bright fringe & `3^('rd)` dark fringe =`9beta-(3beta)/(2)`
`7.5xx10^(-3)=(9-(3)/(2))beta rArr 7.5xx10^(-3)=(9-(3)/(2))(lambdaD)/(d)`
`7.5xx10^(-3)=(7.5xxlambdaxx1)/(5xx10^(-4)) rArr lambda=5xx10^(-7)m`
`lambda=5000Å`