Diffraction by a single slit

The breaking up of a ray of light into dark and light bands or into the colors of the spectrum caused by the interference of one part of the beam with another when the ray is deflected at the edge of an object or passes through a narrow slit is called a single slit diffraction.

Diffraction is the bending and spreading of waves when they meet an obstruction. It can occur with any type of wave, including sound waves, water waves, and electromagnetic waves such as light and radio waves. Diffraction also occurs when any group of waves of a finite size is propagating; for example, a narrow beam of light waves from a laser must, because of diffraction of the beam, eventually diverge into a wider beam at a sufficient distance from the laser. As a simple example of diffraction, if you speak into one end of a cardboard tube, the sound waves emerging from the other end spread out in all directions, rather than propagating in a straight line like a stream of water from a garden hose.

Imagine a plane wave of wavelength , impingent on a barrier with a slit. The barrier transforms the plane wave with infinite extent in the lateral direction into a beam with initial transverse dimensions equal to the width of the slit. In particular, if the slit width is comparable to the wavelength, the beam spreads broadly. If the slit width is large compared to the wavelength, the beam doesn't spread as much. Equation gives us an approximate quantitative result for the spreading angle if is interpreted as the width of the slit. In other words, we can say that Diffraction is an important characteristic of waves. It can be said to one of the defining characteristics of a wave. It occurs when part of a wavefront is obstructed. The parts of the wavefronts that propagate past the the obstacle interfere and create a diffraction pattern. Diffraction and interference are essentially the same physical process, resulting from the vector addition of fields from different sources. By convention interference refers to only a few sources and diffraction refers to many sources or a continuous source.

One use of the above equation is in determining the maximum angular resolution of optical instruments such as telescopes. The primary lens or mirror can be thought of as a rather large ``slit''. Light from a distant point source is essentially in the form of a plane wave when it arrives at the telescope. However, the light passed by the telescope is no longer a plane wave, but is a beam with a tendency to spread. The spreading angle  is given by equation and the telescope cannot resolve objects with an angular separation less than . Replacing with the diameter of the lens or mirror in equation thus yields the telescope's angular resolution. For instance, a moderate sized telescope with aperture observing red light with has a maximum angular resolution of about .

In the picture below has a wavelength of  780nm and the width of the slit is 500nm.

The picture below is about the diffraction when the gap of the slit grows to 5000nm.