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A beam of light consisting of two wavele...

A beam of light consisting of two wavelength `6500Å&5200Å`is used to obtain interferance fringes in a young's double slit experiment .The distance between the slits is `2.0mm` and the distance between the plane of the slits and thescreen is `120cm`,.what is the least distance from the central maximum where the bright fringes due to both the wave length coincides?

A

`0.156cm`

B

`0.152cm`

C

`0.17cm`

D

`0.16cm`

Text Solution

Verified by Experts

Suppose the`m^(th)`brigh fringe of`6500A^(@)` coincides with the`n^(th)`bright fringe of `5200A^(@)`
`X_(n)=(mlambda_(1)D)/(d)=(nlambda_(2)D)/(d)`
`implies (mxx6500xxD)/(d)=(nxx5200xxD)/(d)`
`implies (m)/(n)=(5200)/(6500)=(4)/(5)`
`therefore` distance`y` is`y=(mlambda_(1)D)/(d)`
`y=0.156cm`
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