1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 27: July 31 st 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 Light Waves in Interference O d S2S2 S1S1 y P Q

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Double Slit Interference Conditions Constructive interference: Destructive interference: Small angle approximation:

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 Adding the Electric Field Waves Interference using

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Total Electric Field at Point P A modified amplitude Maximum constructive Interference Total destructive Interference

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 Intensity Distribution of the Double-Slit Interference Pattern Small angle approximation:

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Intensity Distribution of the Double-Slit Interference Pattern

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Example A double slit experiment with a slit separation of 0.500mm is performed with a light containing two prominent spectral lines of wavelengths 589nm (yellow) and 632nm (red). Determine the spatial separation of the first order maximum on a screen that is 5.00m away from the double slit.

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Same example- using small angle approximation

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Phase Change Due to Reflection

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 Interference in Thin Films

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 Conditions for Constructive Interference of Rays 1 and 2 To get constructive interference between rays 1 and 2, they must have a phase difference that is an integer multiple of 2  (360 degrees). Two reasons for phase difference: 1)Ray 1 has phase shift of  due to reflection, or expressed in # of wavelengths: 2)Ray 2 has a phase shift due to the extra distance it has to traverse (2t) (assuming that incident angle is small, so path=2t). Together, for constructive interference, the phase shift expressed as number of wavelengths should be an integer.

13. Physics for Scientists and Engineers II, Summer Semester 2009 13 Conditions for Destructive Interference of Rays 1 and 2 Destructive Interference

14. Physics for Scientists and Engineers II, Summer Semester 2009 14 Interference in Thin Films

15. Physics for Scientists and Engineers II, Summer Semester 2009 15 Conditions for Interference of Rays 1 and 2 Both ray 1 and 2 undergo 180 degree phase shifts: Now you only need to consider the phase shift of ray 2 due to the extra path. Together, for constructive interference, the phase shift expressed as number of wavelengths should be an integer. Destructive Interference Conditions are reversed now !!!!