Snell's Law and Refraction: The Glass Block Experiment
Light bends when it crosses from one material into another, and Snell's Law says by exactly how much.
This page covers refraction, refractive index, the glass block experiment that measures it, and the one mistake that ruins the practical for most classes. Plus the formal assessment project, critical angle and total internal reflection.
Why light bends
Light travels at different speeds in different materials. It is fastest in a vacuum and slower in anything else. Glass slows it to about two thirds of its speed in air.
When a beam crosses a boundary at an angle, one side of the beam enters the slower material before the other side does. That side slows first, and the whole beam swings round.
It is exactly what happens to a trolley that runs onto grass with one wheel first. The wheel on the grass slows, the wheel on the path keeps going, and the trolley turns.
| Going | The ray bends |
|---|---|
| Into a slower medium, air into glass | Towards the normal |
| Into a faster medium, glass into air | Away from the normal |
A ray that arrives along the normal, at 0°, does not bend at all. Both sides of the beam cross the boundary at the same instant, so there is nothing to swing it round.
Refractive index
The refractive index n is how much a material slows light down. The bigger the number, the slower the light and the more the ray bends.
| Medium | Refractive index n |
|---|---|
| Vacuum | 1,00 |
| Air | 1,00 |
| Water | 1,33 |
| Perspex, acrylic | 1,49 |
| Glass | about 1,52 |
| Diamond | 2,42 |
Refractive index has no unit. It is a ratio of two speeds, so the units cancel. Learners invent one surprisingly often and it costs them a mark.
Snell's Law
n1 sin θ1 = n2 sin θ2
where 1 is the medium the light starts in and 2 is the one it enters.
That is the whole thing. Two media, two angles, two indices, and if you know three of them you can find the fourth.
Worked example: air into glass
A ray hits a glass block at an angle of incidence of 40° and refracts to 25° inside the glass. Find the refractive index of the glass.
- n1 sin θ1 = n2 sin θ2
- 1,00 × sin 40° = n2 × sin 25°
- n2 = 0,643 ÷ 0,423
- n2 = 1,52
Worked example: glass into water
A ray travels from glass, n = 1,50, into water, n = 1,33, and refracts at 20° in the water. Find the angle of incidence in the glass.
The light is speeding up, so it bends away from the normal, which means the angle in the water must be the bigger of the two.
- 1,50 × sin θ1 = 1,33 × sin 20°
- sin θ1 = (1,33 × 0,342) ÷ 1,50 = 0,303
- θ1 = 17,6°
Keep three decimals until the last step. Rounding sin 20° to 0,34 partway through gives 17,5° instead of 17,6°, which is close enough to pass and a bad habit on longer problems.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 11 |
| Term | 2 |
| Topic | Geometrical optics |
| Status | FORMAL ASSESSMENT PROJECT |
| Marks | 40 |
The glass block experiment
Shine a narrow beam into a rectangular glass block at three different angles, trace where it goes, and measure the angles.
Apparatus
| Item | Qty |
|---|---|
| Ray box with a single-slit mask | 1 |
| Rectangular glass block | 1 |
| Semicircular glass block, for the formal assessment | 1 |
| Protractor. 0° to 360° for the formal assessment | 1 |
| Plain white paper | 3 sheets per group |
| Sharp pencil and a ruler | 1 |
Three sheets per group is not a typo. Each case needs a clean sheet, and eight groups gets through twenty four sheets plus spares.
Method
- Place the glass block on a sheet of white paper and trace all the way round it in pencil.
- Direct the beam obliquely onto one of the long sides, at a small angle of incidence, about 20°.
- Mark the incident ray, the point where it enters, and the emergent ray with pencil crosses. Two marks on each ray, well apart.
- Repeat on a clean sheet, twice more, with a bigger angle each time. Aim for roughly 20°, 40° and 60°.
- Lift the block off, join up the marks, and draw in the normal at each point of entry, at right angles to the traced edge.
- Measure the angle of incidence and the angle of refraction for the ray going from air into glass.
- Work out sin i ÷ sin r for each case.
What you should see
| Case | Angle of incidence i | Angle of refraction r | sin i ÷ sin r |
|---|---|---|---|
| 1 | 20° | 13° | 1,52 |
| 2 | 40° | 25° | 1,52 |
| 3 | 60° | 35° | 1,51 |
The last column is the result. Three different pairs of angles, and the ratio comes out the same every time. That constant is the refractive index of the glass.
Expect a degree or two of scatter. Protractors read to the nearest degree, pencil lines have width, and the beam is a millimetre or two wide. Anything from about 1,45 to 1,60 is a good result, and a block that comes out at 1,49 is probably Perspex rather than glass.
And one thing to notice
The emergent ray comes out parallel to the incident ray, just shifted sideways.
The beam bends towards the normal going in and away from the normal coming out, by the same amount, so the two bends cancel. It is not obvious and it is examinable.
The formal assessment: verify and apply Snell's Law
The glass block experiment above is the teaching practical. There is a separate formal assessment task, and it is a project.
Two things change when you move to it:
| Teaching practical | Formal assessment project | |
|---|---|---|
| Block | Rectangular | Semicircular |
| Protractor | 180° | 0° to 360° |
| Method | Given | You design your own for Part 2 |
| What you produce | A ratio | A verification, then the refractive index of an unknown material |
Why a semicircular block
Because it removes one of the two refractions.
Stand the block with its flat edge on the diameter of the protractor and aim the ray at the centre of the curve. The ray enters along a radius, so it meets the curved surface at 90° and does not bend at all going in. It only refracts once, at the flat face on the way out.
That makes the geometry far simpler and the measurement far more accurate, which is exactly what an assessed task needs.
Part 1: verify the law
- Put the protractor in the centre of a sheet of A4 and draw in the diameters at 0° and 90°.
- Stand the semicircular block with its straight edge along the 90° diameter, centred.
- Check the alignment first. Send the beam in along the 0° line, which is the normal. If the block is positioned correctly the ray goes straight through without bending at all. If it bends, nudge the block until it does not
- Now take readings at a range of angles and confirm that n1 sin θ1 = n2 sin θ2 holds.
Step 3 is the one to insist on. A ray on the normal that still bends means the block is off centre, and every reading after that will be wrong. It takes ten seconds and it is the difference between a clean set of results and a wasted period.
Part 2: find the refractive index of an unknown
Learners write their own method for this part. Give them a regular shape of some other transparent solid, Perspex or acrylic, and ask for a number.
The answer is the same procedure applied backwards: measure the angles, apply Snell's Law with n for air taken as 1,00, and solve for the unknown.
The mark is for the plan, not the number. A learner who describes repeating at several angles and averaging has understood more than one who gets 1,49 from a single reading.
The mistake that ruins this practical
Angles are measured from the normal. Never from the surface of the glass.
The normal is the dotted line at right angles to the boundary. A learner who measures from the glass edge instead gets 70° where the answer is 20°, and the table, the ray diagram and both calculations all go with it.
The self-check, and it is a good one
If sin i ÷ sin r comes out near 1,0, the angles were measured from the wrong line.
A refractive index of 1,0 would mean the glass slows light exactly as much as air does, which would mean no bending at all. And you just watched it bend.
A result that contradicts what you saw with your own eyes is the most useful kind of wrong answer, and this practical produces it reliably.
Critical angle and total internal reflection
Send light the other way, from glass or water out into air, and it bends away from the normal. Increase the angle of incidence and the refracted ray bends further and further, until it is skimming right along the boundary.
Push past that and the light stops getting out altogether. It all reflects back inside.
The angle where that happens is the critical angle, and the effect is total internal reflection.
Both conditions are needed
- Light must be going from an optically denser medium into a less dense one. Water to air, not air to water
- The angle of incidence must be greater than the critical angle
Almost everyone remembers the second and forgets the first. Going from air into glass, no angle of incidence whatsoever will produce total internal reflection. It simply cannot happen in that direction.
Working out the critical angle
At the critical angle the refracted ray grazes along the surface, so θ2 = 90° and sin θ2 = 1.
Snell's Law becomes n sin C = 1, so sin C = 1 ÷ n.
| Medium | n | Critical angle |
|---|---|---|
| Water | 1,33 | 48,8° |
| Glass | 1,52 | 41,1° |
| Diamond | 2,42 | 24,4° |
Diamond's tiny critical angle is why diamonds sparkle. Light that gets in struggles to get back out and bounces around inside first. That one sentence does more for this topic than a page of theory.
It is also how optical fibres work. Light fired down a glass fibre hits the walls at a shallow angle, well past the critical angle, and reflects perfectly all the way along instead of leaking out.
Seeing it: the second practical
Fill a glass trough with water. Shine the ray box in from the side so the beam refracts into the water and out through the top, and catch it on a white card. Now swing the ray box round slowly so the beam hits the top surface from underneath at a steeper and steeper angle.
At a certain point the emerging beam vanishes and the whole thing reflects back down into the water.
Add a single drop of milk to the water so the beam path is visible. Fluorescein is the usual suggestion and it is not essential, which is fair: it is expensive and it stains everything. Milk works.
If it does not work
| What you see | What caused it |
|---|---|
| No ray, just a pool of light | The single-slit mask is missing from the ray box. The commonest failure of all |
| The ray is too faint to trace | Room too bright. Close the blinds |
| sin i ÷ sin r comes out near 1,0 | Angles measured from the surface, not the normal. Check the diagram, not the arithmetic |
| The ratio is wildly different in each case | The block moved between tracing the outline and marking the rays |
| The ray bends when sent in along the normal | The semicircular block is off centre on the protractor. Nudge it until it does not |
| The emergent ray does not line up | The two marks on one of the rays were too close together |
| The ratio is consistent but about 1,49 | Correct. The block is Perspex, not glass |
| One face gives a blurry beam | That face is frosted or scratched. Turn the block round |
| Nothing happens in the total internal reflection activity | The angle is not large enough yet, or the beam is hitting the top surface from outside rather than from inside the water |
How the 40 marks are made up
| Section | Marks |
|---|---|
| Planning and method | 6 |
| Results and the ratio | 10 |
| Ray diagram | 8 |
| Snell's law calculations | 8 |
| Critical angle and total internal reflection | 4 |
| Conclusion | 4 |
No mark allocation is prescribed for this one. The split above is ours.
The ray diagram is worth 8 on its own, because drawing it correctly is the skill the exam actually tests. Two of those eight are for marking the angles between the ray and the normal, which is the same thing that decides whether the rest of the practical works.
If you have time
Send the beam in along the normal, at 0°. It goes straight through without bending. Learners find that genuinely surprising.
Put a coin in a mug and back away until it just disappears behind the rim. Get someone to pour water in and the coin reappears. No apparatus, thirty seconds, and it is refraction doing exactly what the practical measured.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 40 marks, with the results table, a full-page space for the ray diagram, both Snell's Law calculations and the critical angle question
- Marking memorandum, with worked sample results, a criterion-by-criterion breakdown for the ray diagram, and a note on the six places learners most often drop marks
Related practicals
- The law of reflection. Same ray box, the practical that comes just before this one
- Boyle's Law, Grade 11. Also Term 2
- Intermolecular forces, Grade 11. Formal assessment, Term 1
Apparatus
Everything for this practical lives in the light and optics range: ray boxes, prisms, lenses and blocks.
Two things to check your store cupboard for. The single-slit mask that fits over the ray box, without which there is no ray to trace. And a semicircular block plus a 360° protractor, which the formal assessment needs and the teaching practical does not.