Coherent light with wavelength 594 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. the first-order bright fringe is a distance of 4.84 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 position of bright fringes Y_m on screen in double slit experiment is given by following expressión

We can solve for d, clearing the variables, so

So making the substitution for λ= 594nm, D=3m, y_1=4.84 and m=1, we have

Through this value we can find the position of dark fringes y_m on screen. The following expressión can approach better,

To solve the wavelength m is equal to 0,

clearing for \lambda

Making the substitution for

So we have that the wavelength required is