4.8.1 Refraction

• Refraction occurs when light passes a boundary between two different transparent media
• At the boundary, the rays of light undergo a change in direction
• The direction is taken as the angle from a hypothetical line called the normal
  • This is perpendicular to the surface of the boundaries and is represented by a straight dotted line

• The change in direction depends on which media the light rays pass between:
  • From air to glass (less dense to more dense): light bends towards the normal
  • From glass to air (more dense to less dense): light bends away from the normal
  • When passing along the normal (perpendicular) the light does not bend at all

Refraction of light through a glass block

• The change in direction occurs due to the change in speed when travelling in different substances
  • When light passes into a denser substance the rays will slow down, hence they bend towards the normal

• The only properties that change during refraction are speed and wavelength – the frequency of waves does not change

Calculating Refractive Index

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

• Where:
  • c = the speed of light in a vacuum (m s^–1)
  • v = the speed of light in a substance (m s^–1)

• 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 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 the 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)

Snell's Law

• Snell’s law relates the angle of incidence to the angle of refraction, it is given by:

n₁ sin θ₁ = n₂ sin θ₂

• Where:
  • n₁ = the refractive index of material 1
  • n₂ = the refractive index of material 2
  • θ₁ = the angle of incidence of the ray in material 1
  • θ₂ = the angle of refraction of the ray in material 2

Snell's Law is used to find the refractive indices or the angles to the normal at a boundary

• θ₁ and θ₂ are always taken from the normal
• Material 1 is always the material in which the ray goes through first
• Material 2 is always the material in which the ray goes through second

Aims of the Experiment

• The aim of the experiment is to calculate the refractive index of a transparent semi-circular block

• Independent variable = Angle of incidence, θ₁
• Dependent variable = Angle of refraction, θ₂
• Control variables:
  • Size of the semi-circular block
  • Intensity of light

Equipment List

• Resolution of measuring equipment:
  • Ruler = 1 mm
  • Protractor = 1°

Method

 Apparatus set up to measure the effects of refraction through a semi-circular block

1. Place the semi-circular block on top of the protractor with the centre of its diameter aligned with 0° on the protractor
2. Direct the light from the lightbox towards this 0° and draw a dotted line perpendicular to the long edge of the semi-circular block. This is the normal
3. Using the pencil and ruler, trace the ray entering the block and leaving
4. Repeat this, moving the ray around every 10° up to 80. This is the angle of incidence, θ₁
5. The angle of the ray leaving the block from the normal is the angle of refraction, θ₂. The block should preferably be removed to measure this accurately
6. Record the angle at which the angle of refraction is 90°, (the ray leaves along the straight boundary of the block) just before it is reflected. This is the critical angle
7. Repeat the experiment for the rectangular glass block

• An example table of results would look like this:

Example table of results

Analysis of Results

• The refractive index of the blocks is calculated using Snell's Law:

n₁ sin θ₁ = n₂ sin θ₂

• Since n₁ is the refractive index of the first material, this is air and hence equal to 1
• Therefore, the refractive index of the blocks n is found using the equation:

• Therefore the gradient of the graph of sin θ₂ against sin θ₁ is the refractive index n
• The critical angle, C, can then be calculated using the equation

Example graph of results to measure the refractive index

Evaluating the Experiment

Systematic Errors:

• The lines should be traced from the centre of the light rays each time

Random Errors:

• Use a pencil with a sharp tip to draw the lines on the paper accurately for each angle
• The light from the lightbox will be slightly blurry and dispersed, which gives a subjective reading for the angle
  • Using a concentrate laser light will produce more defined rays so there is less uncertainty when tracing the lines

• Repeat the experiment and find an average reading of each angle of refraction

Safety Considerations

• Do not shine the light from the ray box in eyes as it can damage your eyes
• Lasers can permanently damage your eyesight therefore, wear laser safety goggles
• Don’t shine the laser at reflective surfaces
• Display a laser warning sign on the door
• Never shine the laser at a person
• Make sure the glass blocks are kept away from the edge of the surface of a table, as they could be damaged and crack if they fall