1. Interference and Diffraction

2. Conditions for Interference Coherent Sources - The phase between waves from the multiple sources must be constant. Monochromatic - Wavelength from the sources must be of the same wavelength.

3. Interference Remember the Superposition Principle Constructive Destructive #1 #2 r1r1 r2r2 Source Effect

4. Double Slit Interference Young’s Double-Slit Experiment Two slits act like coherent sources Assumption: d >> Difference in path traveled is Constructive Interference  d 

5. Small Angle Approximation When  << 1, then and d  L y m = 1 m = 2 m = 0 m = -1 m = -2

6. Intensity Phase between waves from slits is Use a phasor diagram to predict the intensity E1E1 E2E2 

7. 1 2 0 -2 Multiple Slits 2 Slits E1E1 E2E2  1 2 0 -2 1 2 0 -2 1 2 0 -2 4 Slits 3 SlitsDiffraction Grating E1E1 E2E2  E3E3 E1E1 E2E2  E3E3 E4E4 Resolving Power

8. Thin Films Constructive interference between waves reflecting off the top and bottom surfaces. 180° Phase Shift 0° Phase Shift t m - whole number

9. Single-Slit Diffraction Huygen’s Principle - Each point along the wave re-emits spherical waves. m = -1 m = -2 d  L y m = 1 m = 2 Destructive Interference Intensity

10. Resolution Rayleigh Criterion - Can resolve two images if the maximum of one image falls on the first minimum of another image. Slit resolution Circular Aperture mm

11. Resolving Detail Detail at a distance can be calculated by What detail can you see at 1 km (10 3 m) with green light (500 nm)? (Let D=0.30cm) r mm s Circular Aperture

12. Interferometer Comparing light from two separate telescopes to increase the resolving power. Very Large Array – Radio TelescopeVery Large Array – Radio Telescope –27 radio antennas in a Y-shaped –Fifty miles west of Socorro, New Mexico –Each antenna is 25 meters in diameter –Resolution of an antenna 36km across –Sensitivity of a dish 130 meters in diameter.

13. Diffraction and Interference Small regularly spaced openings result in bright spots. –Diffraction Grating Spacing of spots depend on distance between openings. –Crystallography