A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment.
What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?
Wavelength of the light beam, lambda_1= 650 nm
Wavelength of another light beam, `lambda_2= 520 nm`
Distance of the slits from the screen = D
Distance between the two slits = d
Let the nth bright fringe due to wavelength `lambda_2` and (n − 1)th bright fringe due to wavelength lambda coincide on the screen. We can equate the conditions for bright fringes as:
`nlambda_2 = (n -1)lambda_1`
`520n = 650n - 650`
650 = 130 n
`:. n = 5`
Hence, the least distance from the central maximum can be obtained by the relation:
`x = nlambda_2 D/d`
`= 5xx582 D/d = 2600 D/d nm`