Question

Please explain why the answer is 0.588 m.

A double slit with a slit separation distance of 2.00 times 10^-5 m is illuminated by light of wavelength 560 nm. If the distance from the slits to the screen is 6.00 m, what is the separation distance between the center of the central bright fringe and the fourth dark fringe above it? Feel free to use the small-angle approximation.

Answer 1

For this case we use the small angle approximation:

$y_m = \frac{(m+1/2)\lambda L}{d}$

The fourth dark fringe is for m = 3

$y= \frac{(3+1/2)(560 \times 10^{-9})(6.00)}{2\times 10^{-5}}= 0.588 m$