In a double slit experiment using a monochromatic light interference fringes are formed on a screen at a particular distance from the slits. If the screen is moved towards the slits by `5 xx 10^(-2)` m then the fringe width changes by ` 3 xx 10^(-5)` m. If the distance between the two slits is `10^(-3)` m then determine the wavelength of the light used.

Explanation

Fringe width `y=(lambdaD)/(2d)`
Here `lambda` is the wavelength of light used D is the distance of the screen from the slits 2d is the separation between the slits. Here screen distance changes by `Delta` D and firnge width changes by `Delta`y.
`:. Delta y =(lambdaDelta D)/(2d)` or , `lambda=(Deltay2d)/(DeltaD)`
Now `Delta y = 3xx 10^(-5) m , 2d =10^(-3)m , Delta D = 5 xx 10^(-2)` m
`:. lambda =(3xx10^(-5)xx 10^(-3))/(5xx10^(-2)) =6xx 10^(-7) ` m =6000 Å