1. The Refraction of Light
SPH4U

2. The Speed of Light

3. Index of Refraction
Light will travel more slowly in more dense materials.
The ratio of the speed of light in a vacuum (or air) to the speed in the material is the index of refraction, n.

4. Index of Refraction: Example
For water, the index of refraction is The speed of light in water is therefore:

5. Index of Refraction: Example
For water, the index of refraction is The speed of light in water is therefore:

6. Index of Refraction: Example
For water, the index of refraction is The speed of light in water is therefore:

7. Frequency and Wavelength
Light with a wavelength of 6.0 x 10-7 m in air (i.e. with a frequency of 5.0 x 1014 Hz) travels into water. What is the frequency of the light in water?

8. Frequency and Wavelength
Light with a wavelength of 6.0 x 10-7 m in air (i.e. with a frequency of 5.0 x 1014 Hz) travels into water. What is the frequency of the light in water? The frequency is the frequency of the original disturbance and therefore remains the same: 5.0 x 1014 Hz

9. Frequency and Wavelength
Light with a wavelength of 6.0 x 10-7 m in air (i.e. with a frequency of 5.0 x 1014 Hz) travels into water. What is the wavelength of the light in water?

10. Frequency and Wavelength
Light with a wavelength of 6.0 x 10-7 m in air (i.e. with a frequency of 5.0 x 1014 Hz) travels into water. What is the wavelength of the light in water?

11. Frequency and Wavelength
Light with a wavelength of 6.0 x 10-7 m in air (i.e. with a frequency of 5.0 x 1014 Hz) travels into water. What is the wavelength of the light in water?

12. Frequency and Wavelength
Light with a wavelength of 6.0 x 10-7 m in air (i.e. with a frequency of 5.0 x 1014 Hz) travels into water. What is the wavelength of the light in water?

13. Boundaries
What happens when a wave meets a boundary between two media?
In 2D (with the boundary at an angle to the wave), the wave will bend as those parts that enter the more-dense material first slow down first.
(The black lines show the crests or “wavefronts”).

14. Please Note!
If the ray is perpendicular to the boundary, no bending will occur:

15. Snell’s Law
The amount by which the wave is bent is given by Snell’s Law (ni and nr are the refractive indices of the media).

16. Snell’s Law
Note that a ray will always bend towards the normal when travelling into a more-dense medium (and away from the normal when travelling into a less-dense medium).

17. Refraction Effects
Refraction effects produce a number of interesting observable phenomena

18. Refraction Effects
Refraction effects produce a number of interesting observable phenomena
E.g. objects in water may appear to be displaced

19. The Broken Pencil
If we look at an object in a different medium, we will see an image of the object along the line of sight of the rays that are refracted to us.

20. Apparent Depth
Similarly, an object underwater will appear to be at a different depth than its actual depth:

21. Total Internal Reflection
But more interesting than the refraction of light rays is the failure of light rays to refract

22. Total Internal Reflection (TIR)
Recall that if a ray is travelling from a more-dense material to a less-dense material it will bend away:

23. Total Internal Reflection (TIR)
So for the case of the ray travelling from the more-dense material to the less-dense material, there must exist some critical incident angle such that the ray will refract at 90o from the normal (along the boundary).

24. Total Internal Reflection (TIR)
If the light is incident at an angle larger than this critical angle qc, total internal reflection will occur.

25. Total Internal Reflection (TIR)
If the light is incident at an angle larger than this critical angle qc, total internal reflection will occur.

26. Total Internal Reflection (TIR)
If the light is incident at an angle larger than this critical angle qc, total internal reflection will occur.

27. Total Internal Reflection (TIR)
If the light is incident at an angle larger than this critical angle qc, total internal reflection will occur.
And remember that nr will be 1.0 if the second medium is air.

28. TIR: Example
When light is travelling through glass into air, the total internal reflection will occur at a critical angle of 42o. Find the index of refraction of the glass.

29. TIR: Example
When light is travelling through glass into air, the total internal reflection will occur at a critical angle of 42o. Find the index of refraction of the glass.

30. TIR: Example
When light is travelling through glass into air, the total internal reflection will occur at a critical angle of 42o. Find the index of refraction of the glass.

31. TIR: Example
When light is travelling through glass into air, the total internal reflection will occur at a critical angle of 42o. Find the index of refraction of the glass.

32. Total vs. Partial
Note that partial reflection will occur at angles less than the critical angle.

33. TIR: An Application
Optical fibres are based on the principle of TIR. An optical fibre is a flexible strand of glass. With a straight or smoothly bending fibre, the light will hit the wall at an angle higher than the critical angle and will all be reflected back into the fibre so that no light will be lost.

34. TIR: Mirages
Air of different densities will have different ns and light rays can reflect within the air, resulting in mirages and looming artifacts.

35. TIR: Mirages
Air of different densities will have different ns and light rays can reflect within the air, resulting in mirages and looming artifacts.

36. TIR: Mirages
Air of different densities will have different ns and light rays can reflect within the air, resulting in mirages and looming artifacts.

37. Dispersion
Different frequencies (colours) of light actually refract at different angles.
This is called dispersion and is especially apparent when white light is passed through a prism.

38. Dispersion in Water Droplets
Dispersion and total internal reflection can occur in water droplets in the air:

39. Dispersion in Water Droplets
which may result in rainbows:

40. More Practice “Snell’s Law Lab” The procedure should be familiar.
The analysis is a little more sophisticated.