Wavelength of the light?

Question

In two separate double slit experiments, an interference pattern is observed on a screen. In the

first experiment, violet light (= 754 nm) is used and a second-order bright fringe occurs at the

same location as a third-order dark fringe in the second experiment. Determine the wavelength of

the light used in the second experiment.

Answer 1

See the ref. First, some definitions of orders and fringes. In interference experiments, the lowest order dark fringe is 0 which occurs at m = 0.5. The lowest order bright fringe is 0 which occurs at m = 0. Subsequent fringes add 1 to m and to the order. So, the 2nd-order bright fringe, m = 2, of λ1, 754 nm = the 3rd-order dark fringe, m = 3.5, of λ2. Then the wavelength ratio λ2/λ1 = 2/3.5, and λ2 = 2*754/3.5 = 430.86 nm.