1. Bendy, Bouncy, Beautiful!
The Path Light Travels
Bendy, Bouncy, Beautiful!

2. When light bends instead of bounces
Refraction
When light bends instead of bounces

4. Refraction
Often, light will not travel in a straight line when it crosses from one transparent medium into another
This is due to the fact that light changes speed when it enters a new medium.
The degree to which it bends is called the angle of refraction; it is measured between the light ray and the normal.

5. Why does light refract?
Well, I don’t know why a change in speed would cause a light beam to swerve from its path
But I do know a good metaphor for it, a metaphor I call the Four Wheel Drive Photon Metaphor

9. Rules of Thumb
Light bends toward the normal when it slows down and away from the normal when it speeds up
The greater the change in speed, the greater the refraction

10. The Refraction Equations
The angle of refraction can be found using this equation:
Sin 2 / sin  1 = 2 /  1
Where 1 and 2 are the two media and  is the speed of light in the respective media
The angles can be incidence and refraction, or 2 refraction angles (to compare two media)

11. Try this problem:
Through which medium does light travel fastest?

12. Answer: Sin glass / sin water = vglass /vwater
Sin 34.5 / sin 40.6 = v2/v1
0.57/ 0.65 = v2/v1
Therefore, vgalss < vwater
Also, you can see that it bends more in glass, so it must be slowing down more in glass

13. Now, try this:
How many times faster does light travel through water than it does through glass?

14. Answer:
Since we want to find out how much faster the speed is in water, vwater /vglass = sinwater /singlass
0.65/0.57 = 1.15, so, it travels 0.15 times faster, or 15% faster

15. Important item: wavelength, frequency, and refraction
As the light changes speed, what happens to the frequency of the light?
Think: if the light changed frequency, how would you know?
It would change color.
So, does the frequency change?
Nope!

16. Important item: wavelength, frequency, and refraction
The light wave changes speed but doesn’t change frequency.
Therefore, what must happen to the wavelength of the light as it goes from space through any other medium?
It must get shorter
Think about what happens to the distance between cars on a freeway when the speed of traffic slows down

17. Index of refraction, n n = c/ 
The index of refraction, n, is the ratio of the speed of light in a vacuum to the speed of light in a transparent medium:
n = c/ 

18. What is the index of refraction in air?
Well, light slows down an itty, bitty, teeny, weeny little bit in air. Basically, the speed in air = the speed in a vacuum
nair = c/v
nair = 3.00 x 108 ms-1/ 3.00 x 108 ms-1
nair = 1.00
Question: what are the units to use?

19. Snell’s Law - a combination of the preceding equations
Indices of refraction for materials are found in published tables. You can use them to find the path of light through various media using this equation:
n1 sin1 = n2 sin  2
The angles are those of incidence and refraction, respectively

20. n1 sin  1 = n2 sin  2 2 n2 n1 1

21. Practice Problem
If nair is 1.00 and nwater is 1.33, then light entering a pond at an angle of 60° to the normal would travel at what angle to the normal through the water?

22. Answer: n1 sin  1 = n2 sin  2 (1.00) sin 60 = 1.33 (sin x)

23. Let’s check:

24. Puzzler
You see a fat, juicy fish in a pond. You are hungry. You throw a rock right at that fish. If your aim is true, do you hit the fish?

25. Fish Puzzler #1

26. Draw the light ray from fish to eye

27. Draw the light ray from fish to eye

28. Trace the thought line backwards

29. The stone misses the fish

30. Puzzler: Where to spear the fish?
We already know that if you throw a spear directly at a fish you see under water, the spear will go over its head
And, the deeper the fish, the greater safety zone it has if you throw straight at the image
So, how do you get that fish?

31. The thought rays meet at
 1 refraction
 2 incidence

32. Equivalent angles
 1 refraction
 2 incidence

33. Quick n dirty:  1 refraction  2 incidence
Apparent depth = real depth / n (water)
 1 refraction
 2 incidence

34. Dispersion - a result of refraction
We already know that the amount that light refracts in a medium depends on its speed
And, we know frequency doesn’t change and wavelength does
So, the amount of refraction can also be considered to be dependent on the wavelength of the light

35. Wavelength in different media
The ratio of wavelengths of light is inversely proportional to the ratio of indices of refraction. This means that, in a material with a larger index, the wavelength of light will be less.
1/ 2 = n2 / n1
This pertains to a beam of light traveling through two different media

36. Puzzler: Which will refract more, red light or blue light?
Which color travels faster in space, red or blue?
Neither! They go the same speed!
Which has a higher frequency, red or blue?
Blue!
So, which has a shorter wavelength?

37. Puzzler: Which will refract more, red light or blue light?
Now, the last equation had to do with one beam of light in two media. But we can also use it to compare two lights in one medium:
red/ blue = nblue / nred
Can you see that blue light has the larger index of refraction?

38. Puzzler: Which will refract more, red light or blue light?
So, nblue > nred
Which has a bigger refraction?
Remember: n1 sin1 = n2 sin2
Rearrange: n1/ n2 = sin 2 / sin 1
Or, nblue/ nred = sin red / sin blue , so
sin red > sin blue
Can you see that red light bends less??

39. Note: light bends toward the normal when it slows down
Red bends away from the straight-line path less than blue light because it has a smaller index of refraction and thus a bigger angle of refraction

40. Dispersion
Dispersion is when refraction causes light to separate into its various wavelengths.
This is commonly called the “prismatic effect”
Rainbows are a product of dispersion

43. Critical Angle and Total Internal Reflection
Total internal reflection: Light reflects completely at an interface, back into the medium with the higher refractive index.
Critical angle: The minimum angle of incidence at which total internal reflection occurs.

44. Why does this happen?
As the angle of incidence increases, the angle of refraction will also increase
n1 sin1 = n2 sin  2
the indices of refraction stay the same
At some point, the index of refraction will equal 90°

45. Critical angle: from water to air
Note: light bends away from the normal when it speeds up

46. air
water

47. air
water
 refracted
The angle of reflection  refracted is 90° to the normal, parallel with the surface of the water. No light escapes.
This is the critical angle,  c

48. When i > c, light does not escape the medium
air
Total internal reflection
water

49. Solving problems with  c
To find the critical angle, use Snell’s law and substitute 90° in for  refracted
n1 sin c = n2 sin  refracted
The sine of 90° is 1, so  refracted = 1
n1 sin  c = n2 1
Or, sin  c = n2/n1