1. Optics: Refraction 3 Learning Objectives
To look further at refraction maths
To understand dispersion
Book Reference : Pages

2. Refraction: Angles Revisited
Incident and emergent rays are parallel
On exit from glass block, new incident ray (i2) is equal to first angle of refraction r1 Similarly for r2 and i1 i1
Medium 1
Medium 2 r1 i2
Medium 1 r2

3. Refraction: Snell’s Law Take 2
We found for the ray at point of entry that :
1n2 = sin i1
sin r1
Where 1n2 is the refractive index between medium 1 and medium 2
However, from symmetry, i2=r1 and r2=i1
So for the emergent ray (medium 2 to medium 1)
2n1 = sin i2 = sin r1 = 1/ 1n2
sin r2 sin i1
Snell’s Law

4. Refraction : Light Speed 1
Refraction occurs because the speed light changes in different materials.
(Note. This does not contravene a relativistic view which says that the speed of light is a constant which can never be exceeded... For a particular single material (e.g. a vacuum) it is a constant which cannot be exceeded. We’re just saying that light in each different material has a particular constant speed which cannot be exceeded for that medium)

5. Refraction : Light Speed 2
Consider a wavefront, which crosses a straight boundary between a vacuum and a glass block Y
vacuum X i r Y’
glass X’

6. Refraction : Light Speed 3
If c is the speed of light in a vacuum and cs is the speed of light in the substance, then the distance travelled in time t is:
For X to X’ is cst (using s=d/t for d)
For Y to Y’ is ct
Now consider the triangle XYY’, Since YY’ is the direction of travel for the wave in the vacuum, which is perpendicular to XY then:
YY’ = XY’ sin i (substituting from above)
ct = XY’ sin i

7. Refraction : Light Speed 4
Now consider the triangle XX’Y’, Since XX’ is the direction of travel for the wave in the substance, which is perpendicular to X’Y’ then:
XX’ = XY’ sin r (substituting from above)
cst = XY’ sin r
Returning to Snell’s law:
sin i = ns = c
sin r cs

8. Refraction : Wavelength
The frequency f of the wave does not change during refraction, However since:
c = f and cs = fs
ns = c = f = 
cs fs s

9. Refraction : Between 2 substances
When a light ray crosses the boundary between materials where light travels at c1 and c2 in each material and they have refractive indices of n1 and n2 then:
sin i = c1
sin r c2
Rearranging and multiply by c: c sin i = c sin r
c1 c2
Since that c/c1 = n1 & c/c2 = n2 substituting :
n1 sin i = n2 sin r “The n sin i rule”

10. Refraction : Critical Angle
We can apply n1 sin i = n2 sin r to TIR and the critical angle: ic
We know that at ic then the angle of refraction r is 90° then :
n1 sin ic = n2 sin 90°
Since sin 90° is 1 then:
Sin ic = n2/n1

11. Optics: Dispersion 1
White light from either a normal bulb or sunlight is made up a continuous range of wavelengths covering the whole spectrum from red (650nm) to violet (about 350nm)
The shorter the wavelength the greater the refraction and so a glass prism will refract different coloured lights by different amounts
We can use a prism to split white light into the full spectrum of colours, we call this dispersion

12. Optics: Dispersion 2
The key characteristic of a prism is that the deviation suffered by the light at the first surface is not cancelled out at the second surface, rather it is added to, unlike a rectangular glass block