User:Inconspicuum/Physics (A Level)/Diffraction

We have already seen why fringes are visible when light passes through multiple slits. However, this does not explain why, when light is only passing through 1 slit, a pattern such as the one on the right is visible on the screen.

The answer to this lies in phasors. We already know that the phasor arrows add up to give a resultant phasor. By considering the phasor arrows from many paths which light takes through a slit, we can explain why light and dark fringes occur.

At the normal line, where the brightest fringe is shown, all the phasor arrows are pointing in the same direction, and so add up to create the greatest amplitude: a bright fringe.

At other fringes, we can use the same formulæ as for diffraction gratings, as we are effectively treating the single slit as a row of beams of light, coming from a row of slits.

Now consider the central beam of light. By trigonometry:

$$\sin{\theta} = \frac{W}{L}$$,

where θ = beam angle (radians), W = beam width and L = distance from slit to screen. Since θ is small, we can approximate sin θ as θ, so:

$$\theta \approx \frac{W}{L}$$

and since λ = d sin θ:

$$\theta \approx \frac{\lambda}{d}$$