1. Agenda Today –Thin Film Interference Friday –Diffraction (Ch. 36)

2. Interference Pattern Path Length Coherent Light Wave - Laser Starting Point Laser / Slit x

3. Interference Pattern Path Length Two Lasers, Two different Starting Points Light on Screen = Laser 1 + Laser 2 Intensity ~ Amplitude Squared (Both Same color) Screen

4. Interference Pattern Path Length Special Case: Two Lasers, Two different Starting Points Light on Screen = Laser 1 + Laser 2 What is intensity of light on screen? Screen

5. Interference Pattern Path Length Special Case: Two Lasers, Two different Starting Points Light on Screen = Laser 1 + Laser 2 What is intensity of light on screen? Screen

6. Interference Conditions Constructive –  x = n Destructive –  x = (n+1/2) = =

7. Different Path Lengths Colors – Oil Slick? Water Oil / Soap

8. Different Path Lengths Colors – Oil Slick? Water Oil / Soap Light can have different Path lengths

9. Different Path Lengths Colors – Oil Slick? Water Oil / Soap If cancel out Blue Light Looks Red…. Path length funny in the oil….

10. What is effective path length difference? Water Oil Oil has thickness t Say angle near normal (looking down) t

11. What is effective path length difference? Water Oil  x   x = 2t? t

12. Take into account index Water, n =1.33 Oil, index n=1.45  x  n   x = 2t t

13. Phase Shift on Reflection (p.1219) Water, n=1.33 Oil, n = 1.45 High n to low n 0 shift Low to High  shift

14. Math – Interference Conditions  x  n ) + R1 + R2,  x = 2t –R1 = phase shift on top reflection (0 or  ) –R2 = phase shift on bottom reflection (0 or  ) Constructive:  = m(2  ), m integer Destructive:  = (m+1/2)(2  ), m integer Case one: air/oil/water system What is minimum thickness for a red film?

15. Math – Interference Conditions Case one: air/oil/water system What is minimum thickness for a red film?  x  n ) + R1 + R2,  x = 2t –R1 = phase shift on top reflection (  ) –R2 = phase shift on bottom reflection (0) Constructive:  = m(2  ), m integer Destructive:  = (m+1/2)(2  ), m integer

16. Math – Interference Conditions Case one: air/oil/water system What is minimum thickness for a red film?  t  n ) +  + 0 –Constructive:  = m(2  ), m integer –Destructive:  = (m+1/2)(2  ), m integer Minimum: What is m? –m = 0 –  t  n ) +  –  t  n ) +  – 2t = 0????

17. Math – Interference Conditions Case one: air/oil/water system What is minimum thickness for a red film?  t  n ) +  + 0 –Constructive:  = m(2  ), m integer –Destructive:  = (m+1/2)(2  ), m integer Minimum: What is m? –m = -1 –  t  n ) +  –  t  n ) +  – 2t = negative????

18. Math – Interference Conditions Case one: air/oil/water system What is minimum thickness for a red film?  t  n ) +  + 0 –Constructive:  = m(2  ), m integer –Destructive:  = (m+1/2)(2  ), m integer Minimum: What is m? –m = 1 –  t  n ) +  –  t  n ) +  –  t  n ) –t = n /2 –See table p. 1220 for quicker conditions.