The fringe width in a Young's double slit inter pattern is `2.4 xx 10^(-4)m`,when a red ligth of wavelength `6,400 overset @A` is used.By how much will it change,if blue ligth of wavelength `4,000 overset@A` is used?

Explanation

For red light:
`beta = 2.4 xx 10^(-4) m`
`lambda = 6400 A = 6400 xx 10^(-10) m`
For blue light:
`beta.`= ?
`lambda. = 4000 A = 6400 xx 10^(-10) m`
We know `beta^(.)/beta = lambda^(.)/lambda` [if `D/d` is constant]
`beta^(.)/(2.4 xx 10^(-4)) = (4000 xx 10^(-10))/(6400 xx 10^(-10))`
`beta^(.) = 10/6 xx 2.4 xx 10^(-4)`
`beta^(.) = 1.5 xx 10^(-4) m`
Change in fringe width `= beta - beta^(.)`
`=2.4 xx 10^(-4) -1.5 xx 10^(-4)`
`=(2.4 -1.5) xx 10^(-4)`
`=0.9 xx 10^(-4) m`
`=0.9 xx 10^(-4) m` (decreases)