### Overview

Diffraction slits, and diffraction gratings in general, are optical components on which coherent light can diffract and interfere with itself to produce a wide variety of interference patterns which are then projected onto a screen.

### Tutorial

The K-Optics __Starter’s Kit__ and both Advanced Kits (__2x1__ and __2x2__) come equipped with 9 different diffraction gratings. Each of which finds use in the Slit Diffraction Experiment. Coherent light is shined upon the slit from a LASER to produce the interference pattern characteristic of that slit which can then be measured.

### Technical Specifications

a. Single Slits

b. Double Slits

c. Special

### Theoretical Background

Diffraction and interference are byproducts of light’s superposition principle. That is, when one light wave meets another light wave, their amplitudes add up. If these waves are coherent then an interference pattern can be readily observed. When coherent waves are identical, nothing very interesting happens apart from pure constructive interference. It is only when the optical path each wave takes is distinct that interference patterns become more interesting.

For two coherent waves – that is, they have the same polarization and wavelength, as well as a constant phase difference between them – we can observe, mathematically, the effect of interference. Suppose two coherent waves of identical amplitudes but different starting locations are given:

We can mark each starting point as the starting phase:

Then, by the superposition principle

and the intensity can be shown to be:

Therefore, for distinct phase differences:

there are distinct effects on the total intensity, in particular:

which is how we get light and dark spots – or, in the case of slits, fringes.

Diffraction from slits is slightly more involved than the one-dimensional demonstration shown above. In general, the pattern projected onto a screen at a distance z due to aperture opening A(x,y) can be calculated by using the Fraunhofer integral:

Where (x',y' ) are coordinates on the aperture, z is the distance to the screen, (x,y) are coordinates on that screen, and λ is the wavelength.

In essence, this integral suggests that the pattern projected on the screen is a Fourier transform of the aperture. This is easily calculable for many different shapes of apertures. Namely, for the single slit case, the result is the famous sinc function which is the Fourier transform of a slit opening (of width b):

Whereas, for the double slit one gets:

Where b is the slit width and d is the separation between the slits.