1. Waves in 2D and 3D
Chapter 8.4

2. Reflection of Waves

3. Key Terms
Incident ray - the ray that strikes a barrier (initial wave/ray).
Reflected ray - the ray that reflects or bounces off the barrier.
Normal Line – a perpendicular line (90°) to the barrier surface
Angle of incidence (θi) - the angle between the incident ray and the normal line.
Angle of reflection (θr) - the angle between the normal line and the reflected ray.

4. Reflection
If a straight wave meets a straight barrier, the wave reflects directly backward (180’).
If a straight wave meets a barrier at an angle, it reflects at an angle.

5. Law of Reflection
The angle of incidence (θi) is equal to the angle of reflection (θr).

6.
Need overhead projector, protractor, light source, blocker of some sort? Refraction: need a glass block

7. Diffraction
The bending/spreading of waves around the edge of a barrier or hole.

8. Diffraction
If waves encounter a barrier with a hole in it, they do not pass straight through. They bend around the edges of the barrier, forming circular waves that spread out.

9. Diffraction
If waves spread around 2 closely-spaced holes, diffraction occurs.
What else occurs?

10. Diffraction

11. Diffraction

13. Diffraction of Sound Waves
We notice sound diffracting around corners or through door openings, allowing us to hear others who are speaking to us from adjacent rooms.

14. Diffraction of Sound Waves – Animal Behaviour
Low-pitched (long wavelength) sounds always carry further than high-pitched (short wavelength) sounds.
Owls are able to communicate across long distances due to the fact that their long-wavelength hoots are able to diffract around forest trees and carry farther than the short-wavelength tweets of songbirds.

15. Echolocation
Bats use high frequency (low wavelength) ultrasonic waves in order to enhance their ability to hunt.
The typical prey of a bat is the moth - an object not much larger than a couple of centimeters. Bats use ultrasonic echolocation methods to detect the presence of bats in the air.
As the wavelength of a wave becomes smaller than the obstacle that it encounters, the wave is no longer able to diffract around the obstacle, instead the wave reflects off the obstacle.
Bats use ultrasonic waves with wavelengths smaller than the dimensions of their prey. These sound waves will encounter the prey, and instead of diffracting around the prey, will reflect off the prey and allow the bat to hunt by means of echolocation.

16. Questions for You
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1) Sketch the wave produced by dipping a finger into water in a ripple tank. Add rays to your diagram to illustrate the directions of the wave movement.
3) Sketch the appearance of a straight wave after it has passed through a small opening in a straight barrier. Add rays to your diagram to illustrate the directions of movement.

17. Questions for You
1) Sketch the wave produced by dipping a finger into water in a ripple tank. Add rays to your diagram to illustrate the directions of the wave movement.
The waves will spread out (surface waves). They will reflect from the sides and then interfere constructively and destructively.

18. Questions for You
3) Sketch the appearance of a straight wave after it has passed through a small opening in a straight barrier. Add rays to your diagram to illustrate the directions of movement.
It will spread around the barrier. It will go through the barrier and make circular surface waves.

19. Refraction
Light bends when it passes through a new transparent medium (like water, glass, etc)
Why?
Light travels at different speeds in different materials. Therefore when the light (or wave) hits the new medium, it changes speed.

20. Refraction
Example. If a toy wagon is rolling on the sidewalk and hits the grass, the wheels meet the grass at an angle.
The direction of
the rolling
wheels changes
when one slows
down before the
other does.

22. Parts of the Wave Incident Wave
Reflected Wave (find angle using Law of Reflection)
Refracted Wave (find angle of refraction using Snell’s Law  symbol = θR)

23. Refraction r R

24. Refraction of Light
Just like with boundaries, waves behave differently when going from a less dense material to a more dense material (or vice versa).
Light twists inward from less to more dense

25. As light rays enter a more dense medium, they travel more slowly and the refracted rays will bend toward the normal line.

26. Refraction
If light rays enter a less dense medium, they travel faster and the refracted rays bend away from the normal line.
Light twists outward from more to less dense

27. Snell’s Law
A ray of light bends in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.
Formula: nisinθi = nRsinθR
where n = refracted index (no unit).

28. Indices of Refraction

29. Example
Light travels from air into an unknown liquid at an angle of incidence of 65.0’. The angle of refraction is 42.0’.
A) Will it bend inward or outward?
B) Make a sketch!
C) Determine the index of refraction (n) of the unknown liquid.

30. Answer A) Inward (less to more dense) B) C) nisinθi = nRsinθR
n= sin65’/(sin42’x ) = 1.35

31. Example
Light travels from air into a ruby crystal at an angle of incidence of 45’.
A) Sketch a diagram.
B) Will the angle of refraction be larger or smaller than 45’?
C) Determine the angle of refraction of the light of the ruby.

32. Answer Air to ruby is less dense to more dense. A) B) Smaller angle
C) Rearrange equation: sinθR = nisin θi/nR = ( )(sin45’)/(1.54) =
θR = 27’