A mixture of light consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interface patterns on the screen. The central maximum of both light coincide. Further it is observed that the third bright fringe of known light coincides with the `4^(th)` bright fringe of the unknown light. From this data, the wavelength of the unknown light is

Options

A. `393.4` nm
B. `885.0` nm
C. `442.5 nm`
D. `776.8 nm`

Answer

C

Explanation

Suppose `.n_(1)` .th bright fringe from light of wavelength `lambda_(1) and .n_(2)` .th bright fringe from light of wavelength `lambda_(2)` are coincides, ,
`:.x_(1)barX_(1)=n_(2)barX_(2)`
`:.n_(1)(lambda_(1)D)/(d)=n_(2)=(lambda_(2)D)/(d)`
`:.n_(1)lambda_(1)=n_(2)lambda_(2)`
`:. lambda_(2)=lambda_(1)(n_(1))/(n_(2))=590xx10(-9)xx(3)/(4)`
`=442.5xx10^(-9)m`
`=442.5 nm`