1. 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) nm (size of Proton)

2. 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) nm (size of Proton)
LIGO 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.

3. Beats
Note: speed of PHASE of the combined wave is DIFFERENT than the speed at which the INTENSITY maximum moves.

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

5. Group Velocity
Constant
Travelling wave

6. 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?

7. 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

8. Michelson Interferometer
Side View t M2
Top View