A micture of light, consisting of wavelength 590nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the scree. The central maximum of both lights coincide. Further, it is obseved that the third bright fringe of known light coincides with the 4th 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

Since, the third bright fringe of known light coincides with the 4th bright fringe of the unknown light
`therefore 3lambda_(1)=4lambda_(2)`
The wavelength of unknown light
`lambda_(2)=(3)/(4) xx 590`
`=(1770)/(4)=442.5nm`