1. The Refraction of Light, the Index of Refraction, and Snell’s Law

2. Refraction
The bending or change in direction of light when it travels from one medium to another.

3. Recall: What Causes Refraction?
Refraction is due to changes in the speed of light.
Different media slow down light by different amounts.
The more that light slows down the more the light is refracted.
When light from the spoon
passes from the water into
the air the light rays are
bent.

4. Recall: Rules of Refraction
1) The incident ray, refracted ray & normal all lie in the same plane
2) When a ray of light passes into a slower, more optically dense medium, the ray of light bends towards the normal. (example air  glass)
3) When a ray of light passes into a faster, less optically dense medium, the ray of light bends away from the normal. (example glass  water)
4) When the angle of incidence is zero, there is no refraction. (No change in direction, yes a change in speed)

5. The Rules of Refraction
Rule #1: The incident ray, normal and refracted ray are all in the same plane.

6. The Rules of Refraction
Rule #2: Light bends towards the normal when its speed decreases in a material.
Medium 2 will have a
slower speed of light
Bends Towards
the Normal

7. The Rules of Refraction
Rule #3: Light bends away from the normal when the speed increases material.
Medium 2 will have
a greater speed of light
Bends away from
the Normal

8. The Rules of Refraction
Rule #4: When the angle of incidence is zero, there is no refraction. (No change in direction, yes a change in speed)

9. Recall: The Index of Refraction
The refractive index of a medium is determined by comparing the speed of light in the medium with the speed of light in a vacuum
Index of refraction of material = speed of light in vacuum
speed of light in medium
Where:
n is the index of refraction
c is the speed of light (vacuum) (always 3.00x108 m/s)
v is the speed of light in a given medium.
The index of refraction has no units because both m/s speeds cancel out.

10. Sample Questions n = 3.00 x 108 m/s 1.52 x 108 m/s n = 1.96 Given:
The speed of light in glass is 1.52 x 108 m/s. What is the Index of Refraction for glass??
Given:
c = 3.00 x 108 m/s
v = 1.52 x 108 m/s
n = ?
n = 3.00 x 108 m/s
1.52 x 108 m/s
n = 1.96
Therefore, the index of refraction of glass is 1.96.

11. Snell’s Law
A formula that uses values for the index of refraction to calculate the new angle that a ray will take as a beam of light strikes the interface between two media.

12. n1sinθ1 = n2sinθ2 Snell’s Law
If you call the indices of refraction of the two media n1 and n2 and call the angles of incidence and the angle of refraction θ1 and θ2 then the formula for Snell’s law is:
n1sinθ1 = n2sinθ2

13. Getting a value for sin using your Calculator
Different calculators may require different inputs for calculating sin
Option 1 (for most):
Press sin then the number corresponding to the angle (i.e. for sin 30° you would type sin then 30)
Option 2:
Other calculators will require you to type the number first then punch in sin (i.e. for sin 30° you would type 30 then sin)

14. Calculating an Unknown Angle
When using Snell’s law, you may end up in a situation where you are looking for the angle only:
0.65 = sinθwater
In such a case, you will have to isolate the angle from the sin symbol in front of it.
To do this you will have to move the sin over to the other side of the equation where it will become sin -1 or the inverse of sin
To calculate this, on most calculators, you will need to press second function and then the sin symbol (look for sin -1)
As for finding sin, depending on your calculator you may have to press sin -1 1st or you may need to punch in the angle first.

15. nwatersinθwater = nzircsinθzirc
Example 1
In an experiment, a block of cubic zirconia is placed in water. A laser beam is passed from the water through the cubic zirconia. The angle of incidence is 50o, and the angle of refraction is 27o. What is the index of refraction of cubic zirconia?
Given:
nwater = 1.33
Θwater= 50o
Θzirc= 27o
Required:
nzirc= ?
Analysis:
n1sinθ1 = n2sinθ2
nwatersinθwater = nzircsinθzirc

16. Example 1 Solve: nwatersinθwater = nzircsinθzirc
1.33 X Sin 50 = nzirc sin 27°
nzirc = 1.33 X sin 50
sin 27°
nzirc = 1.33 X 0.76
0.45
nzirc = 2.25
Paraphrase: The index of refraction for cubic
zirconia is 2.25

17. nairsinθair = nwatersinθwater
Example 2
When light passes from air into water at an angle of 60o from the normal, what is the angle of refraction?
Given:
nair=
nwater = 1.33
Θair = 60o
Required:
Θwater = ?
Analysis:
n1sinθ1 = n2sinθ2
nairsinθair = nwatersinθwater

18. Example 2 Solve: nairsinθair = nwatersinθwater
X sin60° = 1.33 sinθwater
X = 1.33 sinθwater
= 1.33 sinθwater
0.87 = sinθwater
1.33
0.65 = sinθwater
sin = θwater
θwater = 40.5°
Paraphrase: The angle of refraction is 40.5 °

19. Now… 1) Answer Snell’s Law Problems on worksheet
2) Determine the unknown substance!
3) Hand in at end of class