Coherent light with wavelength 597 nm passes through two very narrow slits, and theinterference pattern is observed on a screen a distance of 3.00{\rm m} from the slits. The first-order bright fringe is adistance of 4.84 {\rm mm} from the center of the central bright fringe. For what wavelength of light will thefirst-order dark fringe be observed at this same point on thescreen?

The required wavelength is 1.19 μm

Explanation:

In the double-slit study, the formula below determines the position of light fringes on-screen.

where;

m = fringe order

d = slit separation

λ = wavelength

D = distance between screen to the source

For the first bright fringe, m = 1, and we make (d) the subject, we have:

replacing the value from the given question, we get:

In the double-slit study, the formula which illustrates the position of dark fringes on-screen can be illustrated as:

The value of m in the dark fringe first order = 0

∴

making λ the subject of the formula, we have: