distance between fringes of monochromatic red light

Question

Two parallel slits used for a Young’ s interferometer experiment are 0.5 mm apart. The screen on which, the fringes are projected is 1.5 m from the slits. What is the distance between the fringes for monochromatic red light of wavelength 600 nm? How far is the third dark fringe from the central bright one?

 

Answer is supposed to be (1.8 mm, 4.5 mm), please show me how to calculate.

Answer 1

The distance between fringes is given by the equation y=x*λ/d where x is the distance from the slits to the screen, λ is the wavelength of the light, and d is the distance between the slits.

If we plug in the values given for the distance between two fringes we get (1.5m * 600*10^-9m) / (0.5*10^-3) = 1.8*10^-3m or 1.8mm. Since a dark fringe sits in the middle of each pair of light fringes on the screen, we know the third dark fringe should be halfway between the 2nd and 3rd light fringes (where the central light fringe is the 0th), which are 3.6mm and 5.4mm away from the central light fringe, since we've shown that the distance to the next light fringe is 1.8mm. Then halfway between these is 4.5mm away from the central light fringe.