12.1-12.2 Phase Diff and Interference.pptx

Interference

1. Starter 2. The second glass block is now pressed tightly into contact with the first block. What happens to the ray now? Explain what has happened. Support your answer with a calculation [3] Glass type 2 n = 1.52 Glass type 1 n = 1.55 air 45 ⁰ 1 . After making some calculations draw and label a sketch to show what happens to the ray shown in the glass block [3]

2. Answers 1. A quick calculation shows that 45º is greater than the critical angle and so total internal reflection should take place. The sketch should show an arrowed ray being completely reflected at 45 ⁰ to the normal (by eye) [1] The critical angle is sin -1 (1/1.55) = 40⁰ [2] {M = 1 A = 1 } 2. The ray now leaves the first block and enters the second [1] Explanation – the critical angle for the two blocks is large compared with the glass-air boundary [1] The value of the critical angle for the two blocks in close contact is 79⁰ [2] 1.55sin θ c = 1.52sin90⁰, so sin θ c = 1.52/1.55, θ c = 79⁰ Application is in optical fibres used for communication to reject rays that have long signal paths because they are not travelling directly along the fibre [1]

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4. Waves and phase

5. A reminder As a wave passes through a medium the particles oscillate about their equilibrium position.

6. Displacement Time A A B B O O A B Phase relations The particles in the medium perform one oscillation per wave cycle. One oscillation is equivalent to going once around a circle i.e. through 360 . One wave cycle is therefore equivalent to 360 of phase.

7. Displacement Time A A B B O O Where is the orange point relative to the start of the wave cycle? No. of wavelengths: ¼ λ Angle in degrees 90 A B

8. Displacement Time A A B B O O Where is the orange point relative to the start of the wave cycle? No. of wavelengths: ½ λ Angle in degrees 180 A B

9. Displacement Time A A B B O O A B Where is the orange point relative to the start of the wave cycle? No. of wavelengths: ¾ λ Angle in degrees 270

10. Displacement Time A A B B O O A B When one full wave cycle is complete the particles have passed through 360 phase. We can describe the phase difference between two identical points as 0 or 360 , they are equivalent.

11. Converting to/from radians You must be able to convert between radians and degrees. Key points: there are 2  radians in 360 which is a full wave cycle. So 2  phase is equivalent to a full wave-cycle.    

12. Why radians? If the angle, θ , is measured in radians then the s = r θ . Calculating arc lengths in degrees is trickier so radians simplify the mathematics of waves (and circular motion).

13. Converting to/from radians Key conversions to remember:

14. Phase allows us to describe the relationship between different points on a wave. What is the phase difference in degrees and radians between: Displacement Time N O L M P L & M M & N L & N O & P N & O L & P M & P

15. Measuring phase difference As well as comparing points on the same wave, phase allows us to compare two or more waves. If two waves are shifted by a distance d relative to each other the phase difference is   d

16. In phase Constant phase relationship

17. Constant phase relationship In phase Antiphase A phase difference of π OR 180

18. Constant phase relationship In phase Antiphase A phase difference of π OR 180 Out of phase A phase difference of π /2 OR 90

19. Non-constant phase relationship Occurs when two waves with different frequencies superpose.

20. Questions on phase Draw two waves with a phase difference of: 90 π radians 45 2 π radians π radians 540  

21. Phase Recap Questions Answer phase questions in radians Two points on a wave are apart. What is their phase difference? What type of wave is sound? Describe the motion of air particles as one full cycle of a sound wave travels through them. A sound wave has a wavelength of 34cm. What is the phase difference between two points 100mm apart? How far apart are two points with a phase difference of rad on a radio wave of frequency 90MHz? Two points on a sound wave are 8.5mm apart and have a phase difference of rad. The wave has a frequency of 10kHz, what is the wave speed?         0.42m 340ms -1

22. The Principle of Superposition Superposition of waves – when waves overlap the total displacement is the vector sum of the displacements caused by the individual waves.

23. Superposition visualised https://youtu.be/hw3HkZ77iG4

24. Interference When two waves superpose to produce a a greater or lesser amplitude.

25. Constructive and destructive interference Wave 1 Wave 2 Combined waveform Waves in phase leads to constructive interference Waves in antiphase leads to destructive interference

26. Coherence Waves that have the same frequency and a constant phase difference.

27. Path Difference and Phase Difference Whether two waves of the same wavelength interfere constructively or destructively depends on the phase difference. If the path length difference is an even number of half wavelengths the waves are in phase and constructive interference occurs. If the path length difference is an odd number of half wavelengths the waves are in antiphase and destructive interference occurs.        

28. Multiple source interference patterns Applet Multiple coherent sources of waves will result in an interference pattern with alternating regions of constructive and destructive interference.

29. Thin film interference The light reflected from the top and bottom surface of the film superpose and different wavelengths will destructively/constructively interfere depending on the thickness of the film. Light reflected from the bottom surface travels 2t further than light from the top surface.

30. Thin film interference

31. Thin film interference – Natural Examples

32. Thin film interference – Other Examples

33. Thin-Film Interference for Thickness Measurement A variety of applications require the measurement of thin layers (e.g. making semiconductors for electronic devices). This can be done using devices that take advantage of thin film interference.

34. Look at the diagram of the cuticles on a Blue Morpho butterfly. Why do you think the blue colour is reflected so strongly? How to make colour with holes (Video)

35. CDs

36. Recap - Anti-reflective coatings Look at the diagram to the right. Explain using key terms how the anti-reflective coating reduces the intensity of reflected light.