Light bends at a boundary because its speed changes there
Definition
Refraction
The change in direction of light as it passes from one transparent material into another, caused by a change in its speed at the boundary.
- Light travels fastest in a vacuum and in air, and more slowly in glass, Perspex and water.
- When a ray meets the boundary at an angle, one side of the beam enters the glass and slows down while the other side is still travelling fast in the air.
- That lagging side pivots the whole beam round, exactly like a trolley slewing sideways when one wheel hits gravel before the other.
- Going from a faster material into a slower one, the ray bends towards the normal.
- Going from a slower material into a faster one, it bends away from the normal.
- The frequency of the light never changes, so the colour stays the same; it is the speed and the wavelength that change together.
Both angles are measured from the normal, never from the surface
Definition
Normal
A construction line drawn at right angles (90∘90^\circ90∘) to a boundary, at the point where the ray meets it.
Definition
Angle of refraction
The angle between the refracted ray and the normal, measured inside the second material. Symbol rrr.
- The angle of incidence, iii, is the angle between the incident ray and the normal, on the air side of the boundary.
- Going from air into glass, the ray bends towards the normal, so rrr is smaller than iii.
- Going from glass back into air, the ray bends away from the normal, so the angle in the air is larger than the angle in the glass.
- A ray that meets the boundary along the normal has i=0∘i = 0^\circi=0∘, so it slows down but carries straight on with no bending at all.
- Increasing iii increases rrr, but the two are not in proportion, so doubling iii does not double rrr.
Through a rectangular block, the light comes out parallel but shifted
- A rectangular block has two parallel faces, so the light crosses two boundaries and is refracted twice.
- At the first face it slows and bends towards the normal.
- Inside the glass it travels in a straight line, because nothing changes along the way.
- At the second face it speeds up and bends away from the normal by the same amount.
- The two bends are equal and opposite, so the emergent ray is parallel to the incident ray but shifted sideways along the block.
- That sideways shift is called lateral displacement, and it grows with a thicker block or a larger angle of incidence.
- Looking through a thick block at a pencil behind it, the pencil appears jumped to one side, which is lateral displacement seen directly.
Practical
Investigation: tracing rays through a transparent block
- Aim: to trace the path of a ray of light through transparent blocks of different shapes and to measure the angles of incidence and refraction.
- Apparatus: a ray box or lamp with a single narrow slit, a rectangular glass or Perspex block, a triangular prism and a semicircular block, a protractor, a 30 cm30\ \text{cm}30 cm ruler, a sharp pencil and plain paper.
- Method:
- Stand the rectangular block on the paper and draw carefully round it, so you can put it back in exactly the same place later.
- Mark a point O\text{O}O near the middle of one long face and draw the normal there as a dashed line at 90∘90^\circ90∘ to that face.
- Darken the room and shine the ray at O\text{O}O so that the angle of incidence is about 20∘20^\circ20∘.
- Mark two crosses far apart on the incident ray and two more on the ray emerging from the far face, without moving the block.
- Lift the block away, join each pair of crosses, then join the entry point to the exit point to reveal the path inside the glass.
- Repeat for angles of incidence of about 30∘30^\circ30∘, 40∘40^\circ40∘, 50∘50^\circ50∘ and 60∘60^\circ60∘, using a fresh sheet or a fresh outline each time.
- Swap the rectangular block for the prism and then the semicircular block, tracing the ray through each in the same way to compare the paths.
- Measure and plot: measure iii and rrr from the normal at the first face and tabulate them under i / degrees and r / degrees; also check with a ruler that the emergent ray is parallel to the incident one.
- Result: rrr is always smaller than iii on entering the block and both grow together; a ray sent in along the normal passes straight through; and the emergent ray from the rectangular block is parallel to the incident ray but laterally displaced.
- Extension: the same table of iii and rrr values is used to calculate the refractive index of the glass from n=sini/sinrn = \sin i / \sin rn=sini/sinr.
- Watch out:
- The block must not shift between marking the entry and exit rays, so hold it down and draw round it before you start.
- Use small angles of incidence and the bend is tiny, so a 1∘1^\circ1∘ marking error matters a lot; take readings up to about 60∘60^\circ60∘ to keep the percentage uncertainty down.
- Mark the centre of the bright band with a sharp pencil, and put the two crosses as far apart as the paper allows.
- Safety: the ray box lamp gets hot, so let it cool before you move it, and never look straight into the beam.
Different shapes bend the light in different ways
- A triangular prism has faces that are not parallel, so the two bends do not cancel and the emergent ray leaves in a genuinely new direction.
- A semicircular block is used with the ray aimed at the centre of its flat face, so the ray enters through the curved side along a radius.
- A radius is always along the normal to the curved surface, so the ray enters without bending and only refracts once, at the flat face.
- Whatever the shape, the same rule is being applied at every boundary: work out the normal at that point, then bend towards it or away from it depending on which way the speed changes.
Example
- A straw standing in a glass of squash looks bent at the surface of the drink.
- Light from the submerged part of the straw speeds up as it leaves the liquid and bends away from the normal.
- Your eye traces those rays back in a straight line, so the underwater part appears higher and shifted sideways.
- The same effect makes a swimming pool look shallower than it really is.
Common Mistake
- Do not say light bends because the glass is denser; the mark is for the change in speed.
- Do not draw the ray bending inside the block; it travels in a straight line between the two faces and bends only at the boundaries.
- Do not bend a ray that arrives along the normal, because there is nothing to make it turn.
- Do not measure the angle of refraction from the glass surface; it is measured from the normal, like every other optics angle.
- Do not write that the emergent ray is the same as the incident ray; it is parallel to it, but displaced sideways.
Exam technique
- Draw the normal at each face before you draw the refracted ray, and dash it so it is not mistaken for light.
- In a completion question the marks are usually one for bending the right way at each face and one for the emergent ray being parallel to the incident ray, so check all three before you move on.
- Describing the experiment is point-marked, so name the ray box, the outline drawn round the block, the marked crosses and the protractor rather than writing "shine light through the glass".
- When an explanation is asked for, give the full chain: the speed changes at the boundary, so the direction changes, and it bends towards or away from the normal.
Self review
- What causes light to change direction when it enters a glass block?
- Define the angle of refraction.
- Describe the path of a ray of light entering a rectangular glass block at 40∘40^\circ40∘ and leaving through the opposite face.
- What happens to a ray that meets a boundary along the normal, and why?
- Why does a ray aimed at the centre of the flat face of a semicircular block enter the curved side without bending?
