1. Unit 2 Particles and Waves Refraction
CfE Higher Physics
Unit 2
Particles and Waves
Refraction

2. Learning Intentions
State that the ratio sinθ1 /sinθ2 is a constant when light passes obliquely from medium 1 to medium 2
Carry out calculations using the relationship for refractive index
State the absolute refractive index, n, of a medium is the ratio sinθ1 /sinθ2, where θ1 is in a vacuum (or air as an approximation) and θ2 is in the medium.

3. Refraction
Refraction is the change in speed of a ray of light as it passes from one material into another.
This change in speed often results in a change in direction.
As light travels from a fast medium (e.g. air) into a slow medium (e.g. glass) it tends to bend towards the normal.

4. Refraction (continued)
normal
incident
ray qa
material
air qm
refracted
ray

5. Snell’s Law n is the refractive index of the material.
sinqa
sinqm
= n
n is the refractive index of the material.
n is always greater than 1.

6. Worked Example
A ray of light passes from air into glass, as shown in the diagram below. Calculate the angle of the refracted ray inside the glass block. The refractive index of the glass is 1.48.
sinqa
sinqg
= n
50°
air
glass
26°
sin 40°
sinqg
= 1.48
40°
qg = 26°

7. Learning Intentions
State that the refractive index depends on the frequency of the incident light.
State that the frequency of a wave is unaltered by a change in medium
State the relationships for refraction of a wave from medium 1 to medium 2:
Carry out calculations using the above relationship.

8. Refractive Index and Frequency
The refractive index of a medium depends on the frequency (colour) of the incident light.
The refractive index for violet light is slightly greater than that for red light.
When white light enters a prism it is separated into it’s component colours to form a spectrum.
Red
Orange
Yellow
Green
Blue
Indigo
Violet
white light

9. Refractive Index, Speed and Wavelength
The speed and wavelength of light depend on the refractive index of the medium.
sinqa
sinqm
n = va vm = la lm =
The frequency of light is not affected by the medium.

10. Worked Example
Light with a wavelength of 520 nm passes from air into water. Water has a refractive index of Calculate the wavelength of the light in water la lw
= n
520 x 10-9 lw
= 1.3
lw = 4.00 x 10-7 m
= 400 nm

11. Learning Intentions Explain what is meant by total internal reflection
Explain what is meant by critical angle θc
Derive the relationship sinθc = 1/n, where θc is the critical angle for a medium of absolute refractive index, n.
Carry out calculations using the above relationship

12. Critical Angle
When a ray of light passes from a slow medium (high refractive index) into a fast medium (low refractive index) it refracts away from the normal.
If the angle inside the slow medium is increased, a point is reached where the angle in the fast medium becomes 90°. This angle is known as the critical angle, qc.
If the angle in the medium is greater than the critical angle then no light is refracted and total internal reflection takes place.

13. Critical Angle (continued)
sinqa
sinqm
n =
air
medium
90°
sin90°
sinqc
n = qc 1
sinqc
n =

14. Worked Example
A ray of light inside a perspex block is incident to the boundary with air at an angle of 58°. The refractive index of perspex is Complete the diagram below to show the path of the ray.
sinqc = n 1
sinqc =
1.42 1
air
perspex
58°
58°
qc = 45°
Since 58° > qc total internal reflection takes place.