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A beam of light consisting of two wavelengths 800 nm and 600 nm is used to obtain the interference fringes in a Young's double slit experiment on a screen placed 1.4m away. If the two slits are separated by 0.28 mm, calulate the least distance from the central bright maximum where the bright fringes of the two wavelengths coinside.

Text Solution

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`(n_(1)lambda_(1)D)/(2d)=(n_(2)lambda_(2)D)/(2d)` [2d= distance between the slits]
or `(n_(1))/(n_(2))=(lambda_(2))/(lambda_(1))=(600)/(800)=(3)/(4)`
`:.` 3rd order of 800 nm will overlap with 4th order of 600 nm.
`:.` Distance of the point from central bright maximum
`y=(n_(1)lambda_(1)D)/(2d)=(3xx800xx10^(-9)xx1.4)/(2.8 xx10^(-4))`
`=12xx10^(-3)`m =12mm
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