Trivia Question In class we talked about using interference to measure the thickness of thin films. In general, optical instruments which use the interference effect to measure thicknesses or distances are called ‘interferometers’. What is the SMALLEST distance ever measured with an interferometer? (a) 100×10-6 m (width of human hair) (b) 1×10-6 m=1000nm (single cell algae) (c) 10 nm (thickness of cell wall) (d) 0.1 nm (size of atom) (e) 0.88 10-6 nm (size of Proton)

Trivia Question In class we talked about using interference to measure the thickness of thin films. In general, optical instruments which use the interference effect to measure thicknesses or distances are called ‘interferometers’. What is the SMALLEST distance ever measured with an interferometer? (e) 0.88 10-6 nm (size of Proton) LIGO - http://www.ligo.org/ - Laser Interferometer Gravitational-Wave Observatory ….can detect a change in the 4 km mirror spacing of less than a ten-thousandth the charge diameter of a proton, equivalent to measuring the distance to Proxima Centauri with an accuracy smaller than the width of a human hair.

Beats Note: speed of PHASE of the combined wave is DIFFERENT than the speed at which the INTENSITY maximum moves. http://optics.byu.edu/animation/Beats.mov

Beats https://www.youtube.com/watch?v=yia8spG8OmA For BEATs, the AMPLITUDE of the TOTAL wave is modulated at a frequency of https://www.youtube.com/watch?v=yia8spG8OmA For a practical example, its easiest to ‘hear’ with acoustical waves rather than electromagnetic waves.

Group Velocity Constant Travelling wave

Group Velocity versus Phase velocity For animation below, GREEN dot follows position of GROUP of waves. Note: follows speed at which the envelope of wave motion travels. RED dot follows constant PHASE within the wave. Note that PHASE and GROUP velocity in general are DIFFERENT. Which speed determines Velocity at which INFORMATION can be transmitted? Which velocity can be LARGER than speed of light?

Michelson Interferometer Change constructive/ destructive interference by changing RELATIVE path length of L1 and L2 For analysis, CONCEPTUALLY assume that mirrors are BEHIND each other so rays are collinear. L2 L1 DL

Michelson Interferometer Side View t M2 Top View