A micture of light, consisting of wavelength 600nm 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. 450 nm
B. 776.8 nm
C. 393.4 nm
D. 885.0 nm

Answer

A

Explanation

third bright of known light
`X_(3)=(3lamda_(1)D)/(d)` .(1)
`4^(th)` brigt of unknown light
`X_(4)=(4lamda_(2)D)/(d)` ..(2)
Given `X_(3)=X_(4)`
`3lamda_(1)=4lamda_(2)`
`lamda_(2)=(3)/(4)lamda_(1)=(3)/(4)xx590=442.5nm`