Refraction at a Plane Surface (AQA A Level Physics): Revision Note

Refractive index

• The refractive index of a material is the ratio of how fast light travels through that particular substance compared to the speed of light in a vacuum

Refraction

• Refraction is:

  The change in direction of a wave when it passes through a boundary between mediums of different density

• This change of direction is caused by a change in the speed of different parts of the wavefront as they hit the boundary

  • In optics, the word medium is used to describe a transparent material

Conditions for refraction

• The more optically dense the medium, the slower the waves travel and the smaller the angle of refraction

  • The light bends towards the normal

• The less optically dense the medium, the faster the waves travel and the larger the angle of refraction

  • The light bends away from the normal

• The amount of refraction that takes place is determined by the difference between the angles of incidence (i) and refraction (r) of the waves at the boundary

• The angles of incidence and refraction are measured from the normal line 

  • This is drawn at 90° to the boundary between the two media

• The amount of change in direction that takes place depends on the difference in optical density between the two media

• When light passes from a less dense medium to a more dense medium, (e.g. air → glass):

  • The refracted light has a lower speed and a shorter wavelength than the incident light 

• When light passes from a more dense medium to a less dense medium (e.g. glass → air):

  • The refracted light has a higher speed and a longer wavelength than the incident light

• When a wave refracts, its speed and wavelength change, but its frequency remains the same

  • This is noticeable by the fact that the colour of the wave does not change

• When the light ray is incident on the boundary at 90°:

  • The wave passes straight through without changing direction

  • This is because the whole wavefront enters the boundary at the same time

Refractive index

• The refractive index, $n$, is a property of a material which measures how much light slows down when passing through it

• The refractive index of a material is calculated using the equation: 

$n=\frac{c}{c_s}$

• Where:

  • $n$ = refractive index of material 

  • $c$ = the speed of light in a vacuum (m s^–1)

  • $c_s$ = the speed of light in a substance (m s^–1)

• Note that, being a ratio, the absolute refractive index is a dimensionless quantity

  • This means that it has no units

• Light travels at different speeds within different substances depending on their refractive index

  • A material with a high refractive index is called optically dense, such a material causes light to travel slower

• Since the speed of light in a substance will always be less than the speed of light in a vacuum, the value of $n$ is always greater than 1

• In calculations, the refractive index of air can be taken to be approximately 1

  • This is because light does not slow down significantly when travelling through air (as opposed to travelling through a vacuum)