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Refraction at a Plane Surface

Physics: AQA A Level, topic 3.2.7

Refractive Index

Light changes speed and bends when it passes from one medium to the next. This is called refraction.

Change of speed

Change of speed

  • When light passes from one medium to the next, it changes speed.
  • In a vacuum (empty space), light travels at speed c = 3×108m/s.
  • Light travels more slowly in all other materials.
  • The refractive index, n, of a material is the ratio of the speed of light in a vacuum, c, to the speed of light in that material, cs. It is given by:
  • n=ccsn = \frac{c}{c_s}
Refractive index of air

Refractive index of air

  • Air contains lots of chemicals and elements such as oxygen and nitrogen.
  • However, the speed of light in air is so close to the speed of light in a vacuum, that we can approximate them to be the same:
  • cair ≈ c
  • Therefore the refractive index of air is approximately 1.

Snell's Law

Snell's law relates refractive indices to the angles of incidence and refraction.

Equation

Equation

  • Snell's law is:
  • n1sin⁡θ1=n2sin⁡θ2n_1 \sin \theta_1 = n_2 \sin \theta_2
  • The ray of light begins in the medium with refractive index n1.
  • θ1 is the angle of incidence.
  • n2 is the refractive index of the medium the light passes into.
  • θ2 is the angle of refraction.
Direction of bending

Direction of bending

  • When light travels from a less optically dense medium to a more optically dense medium, it bends towards the normal.
  • When light travels from a more optically dense medium to a less optically dense medium, it bends away from the normal.
  • The more optically dense a medium is, the slower light travels through it, and therefore the larger its refractive index.

Critical Angle

When light travels from a medium with a high refractive index (more optically dense) to a medium with a low refractive index (less optically dense) at the critical angle, it will be entirely reflected.

Equation

Equation

  • The critical angle, θc occurs when:
  • sin⁡θc=n2n1\sin \theta_c = \frac{n_2}{n_1}
  • Where n1 is the more optically dense material and n2 is the less optically dense material.
Total internal reflection

Total internal reflection

  • At angles of incidence larger than or equal to the critical angle, no light is refracted.
  • Instead, all the light is reflected.
  • This is called total internal reflection.

Test yourself on Refraction at a Plane Surface

  • What do we approximate the refractive index of air to be?

  • Which of these statements are true about refractive indices?

  • What is the correct equation for Snell's law?

  • What is the equation for the critical angle?

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