## Basic Interferometry:

(Based on a summer student project done by Steven Johnsen and Paul Fulda 2007)

# Introduction

Light has both particle and wave characteristics. It transfers energy like a particle but propagates like a wave. Interferometry can display the wave-like nature of light. Waves can interfere when they came overlap with each other. The two extreme cases are constructive interference and destructive interference in which the to waves add into one with double amplitude or zero amplitude respectively. The kind of interference is determined by the relative phase between the two waves

When light beams are separated and brought together one of the beams will usually have a phase change with respect to the other beam. This phase can be measured by looking at the interference of the two beams. A simple example of this is theYoung's slits experiment.

# Albert Michelson

Albert Michelson was awarded the Nobel Prize for Physics in 1907 for his development of the interferometer and the work with Edward Morley in measuring the electromagnetic aether. At the turn of the 1900 the belief was that electromagnetic waves such as light and radio waves traveled in some substance called electromagnetic aether. By measuring the speed of light in different directions one would expect to obtain different results due to the movement of the Earth through the aether causing a relatve change in velocity of the aether.

The experiment always measured the same speed of light, thus disproving the existence of the aether. This lead to the postulate that the speed of light is constant and thereby the creation of the Special Theory of Relativity.

# Michelson Interferometer

A part of the teaching of interferometery was a student project to build a Michelson interferometer. The purpose of the interferometer was as to create a teaching aid and a display to explain the interference of light. The interferometer can be used to measure the variation of the position of one of the mirrors. The frequency of the sound it emits when the handle is turned is equal to the frequency with which the interference fringes at the photodiode change as the mirror is moved.

The interferometer works by splitting a laser beam into two beams, reflecting them back of two mirror and then recombining the beams again with the same beam splitter. If the distance they have traveled is not the same, their relative phase will non-zero. If this phase is equal to a integral multiple of wavelengths then the beams will interfere constructively, if the phase is equal to an integral multiple plus one half a wavelength, then they will interfere destructively.

When the micrometer wheel is rotated, mirror 4 moves, changing the distance one of the beams has to travel. By moving the wheel very slowly one can observe how the light on the photodiode changes between bright and dark, illustrating the constructive and destructive interference respectively. If you move the wheel quickly the rate of change between the states becomes very fast. The signal from the photodiode is amplified and played through the speaker. If you turn the wheel fast then some sound will be heard; the frequency of the sound will be the same as the rate of change between the dark and bright states. If you spin the wheel faster a higher frequency will be heard.