Diffraction

In sound and water, wavelengths have measurable size.

Coherent sources are needed with equal wavelength and frequency, using the same oscillator for both sources. 

For water, one oscillator drives two dippers.

Use two light sources which are coherent, or a single laser, and shine through 2 slits. 

Light from a laser is coherent and monochromatic. 

Slits must be the same size as the wavelength of the laser light so light is diffracted.

A pattern of light/dark fringes is made. 

Thomas Young, using the sum, came up with a formula for the wavelength of light. 

Measure fringe spacing, x. 

Replace the laser and slits with two microwave transmitter cones attached to a signal generator.

Replace the screen with a receiver probe.

Move the probe along the path and obtain a pattern for strong and weak signals. 

Fringes are tiny, so it's hard to get an accurate measure to obtain the wavelength. To reduce percentage uncertainty, divide the number of fringes by length, L. 

In the 17th century, Isaac Newton issued his corpuscular theory that light is made of corpuscles, explaining reflection and refraction. 

Huygens issued his wave theory of diffraction. Young's Double Slit experiment, 100 years later, proved that lights are waves as they diffract and interfere. 

Bright bands are brighter and dark bands darker. Monochromatic light passes a grating with hundreds of slits per mm. As so many beans reinforce the pattern, it's very sharp and so measurements are more accurate. 

For monochromatic light, all maxima are bright lights, and maximum brightness occurs at zeroth order.

If there are N slits, spacing (d)= 1/N metres.

At each slit, waves are diffracted and the waves interfere with each other to produce an interference pattern. 

At the first order maximum, this occurs at an angle where waves from one slit line up with waves from the next slit one wavelength behind. 

If wavelength is larger, sin0 is bigger, so the angle is bigger. The pattern spreads out. 

If d is bigger, sin0 is smaller, so the coarser the grating, the smaller the pattern. 

Values of sin0>1 are impossible, so these orders must not exist. 

Small angle approximations can be used to relate tan0=x/L to sin0=wavelength/d 

White light is a mixture of wavelengths. When it is diffracted, patterns due to different wavelengths spread differently, with each order forming a spectrum with red on the outside and white on the inside. Each order becomes a spectrum with red furthest from the maxima at the zeroth order, and white at this order as all wavelengths are in phase. 

This is studied by astronomers and chemists for spectra as diffraction is more accurate than prisms, to identify elements of stars.