Can We Make Light Turn Back? From Refraction to Optical Fibres

Put a pencil into a glass of water and it appears bent. Shine a narrow beam into a transparent block and its direction changes. Keep adjusting the experiment, however, and something more surprising happens: the light stops emerging through one surface and returns into the block.

There is no silver coating. No mirror has been added.

The boundary itself produces total internal reflection.

This is an experiment I would build a whole lesson around. It connects observation, careful measurement and mathematical prediction, then leads naturally to the optical fibres that carry information as light.

The journey is:

Reflection → refraction → critical angle → total internal reflection → optical fibres.

The real value comes from letting students discover why each stage follows from the previous one.

Begin with Snell’s Law — and Give the Symbols Meaning

Snell’s law describes what happens when light crosses a boundary between materials:

n1 x sin(i) = n2 x sin(r)

Here:

• n1 is the refractive index of the material the light is travelling from;
• n2 is the refractive index of the material it is entering;
• i is the angle of incidence;
• r is the angle of refraction.

Both angles are measured from the normal: an imaginary line perpendicular to the surface where the ray meets it.

They are not measured from the surface itself.

Refractive index relates the speed of light in a material to its speed in a vacuum:

n = speed of light in a vacuum / speed of light in the material

For an oblique ray, entering a higher refractive index material bends the ray towards the normal. Entering a lower refractive index material bends it away. At normal incidence, light can change speed without changing direction. OpenStax

I would introduce the equation alongside a visible beam. Before students enter numbers into a calculator, ask them to point to the angles the symbols describe.

That small step can reveal a misunderstanding before it becomes a page of incorrect calculations.

What You Need

For an investigation lasting around 45–60 minutes:

• A school ray box with a single narrow slit.
• A semicircular transparent acrylic block.
• A small plane mirror.
• Plain paper, a sharp pencil, ruler and protractor.
• A calculator in degree mode.
• White card to help locate emerging light.

A rectangular block is useful for investigating refraction, but a semicircular block makes the transition to total internal reflection easier to control.

Work in subdued lighting while keeping enough light to read instruments and move safely. Keep beams below eye level and never look into the source or emerging rays. A ray box is sufficient; lasers require appropriate educational equipment, beam stops and their specified safety controls. Ray-box lamps can become hot.

A practical observation: the beam may be easier to follow across the paper than inside a very clear block. Mark the visible incident and emerging paths, then reconstruct the internal ray.

Stage 1: Establish the Law of Reflection

Stand the mirror along a line drawn on the paper.

Direct the ray towards it and mark two points along both the incident and reflected paths. Draw the normal at the point of incidence and measure the angles.

Angle of incidence = angle of reflection

Repeat at several angles.

Then ask:

“If we replace the mirror with a transparent surface, will all the light pass through?”

Students may expect transparent materials to transmit everything. Looking for a reflected ray as well as a refracted ray makes the next stage more interesting.

Stage 2: Measure Refraction from Air into Acrylic

Place the semicircular block on the paper and trace its outline.

Mark the midpoint of its flat face. This is the centre of the circle from which the block was cut. Draw a normal through that point.

Direct the beam from air onto the midpoint of the flat face, initially at about 20 degrees to the normal.

Mark:

• Two points along the incident ray.
• The point where the light leaves the curved face.

Because the internal ray starts at the circle’s centre, it reaches the curved face along a radius. It therefore meets that face normally and leaves without another change of direction.

Remove the block and draw the internal path from the midpoint to the exit point. Measure the incidence and refraction angles at the flat face.

Repeat for incident angles of approximately 30, 40, 50 and 60 degrees, replacing the block accurately each time.

Turn measurements into a refractive index

Suppose you measure:

i = 40 degrees

r = 25.5 degrees

Taking the refractive index of air as approximately 1:

n_acrylic = sin(i) / sin(r)

n_acrylic = sin(40 degrees) / sin(25.5 degrees)

n_acrylic = approximately 1.49

These are illustrative values, rather than results students should be expected to reproduce exactly.

For a stronger investigation, plot:

Vertical axis: sin(i)

Horizontal axis: sin(r)

For air-to-acrylic measurements, the gradient estimates the acrylic’s refractive index.

Ask why a graph using several measurements is generally more persuasive than one apparently perfect result.

Stage 3: Reverse the Journey

Now arrange for the light to travel inside the acrylic towards the flat acrylic–air boundary.

This is essential.

Simply increasing the angle of a beam entering acrylic from air will not produce total internal reflection at that entry surface.

Leave the block on its outline. Send the beam into the curved face, aiming along a radius towards the midpoint of the flat face.

The beam enters the curved face along its local normal, so it does not change direction there. Its first significant change of direction occurs when it reaches the flat face from inside.

Begin with a small internal incidence angle.

The emerging ray bends away from the normal.

Now move the source around the fixed block, always keeping the beam aimed along a radius towards the same midpoint. Increase the internal incidence angle in small steps.

Measure that angle at the flat face, inside the acrylic.

Do not measure it against the curved surface.

Stage 4: Find the Critical Angle

As the internal incidence angle increases, the emerging ray approaches the flat surface.

Near the transition, make smaller adjustments and use white card to locate the emerging beam.

At the critical angle, the refracted angle reaches 90 degrees to the normal. In the ideal ray diagram, the refracted ray runs along the boundary.

Above this angle, total internal reflection occurs. The two requirements are:

• Light approaches the boundary from the higher refractive index material.
• Its incidence angle exceeds the critical angle. OpenStax

In practice, a beam has finite width and some spread of directions. The transition may look less sharp than a textbook drawing.

Record a small angular range within which the emerging beam disappears, rather than claiming unrealistic precision.

Predict the turning point

At the critical angle, substitute r = 90 degrees into Snell’s law:

n1 x sin(c) = n2 x sin(90 degrees)

Since sin(90 degrees) = 1:

sin(c) = n2 / n1

For acrylic with refractive index 1.49, surrounded by air:

sin(c) = 1.00 / 1.49

c = inverse sine(1.00 / 1.49)

c = approximately 42.2 degrees

Use the inverse sine function with the calculator in degree mode.

Now compare prediction and observation.

Does 42.2 degrees fall within the transition range you recorded? If it does not, check the alignment and angle measurements before deciding the physics has failed.

Stage 5: Watch the Light Return

Increase the internal incidence angle beyond the critical angle.

The light reflects back into the acrylic at the flat surface.

Look for its subsequent exit through the curved face. Total internal reflection at one boundary does not mean the beam remains trapped inside the entire block indefinitely.

The reflected ray still obeys:

Angle of incidence = angle of reflection

I particularly like the teaching opportunity here. A student who predicts the transition before observing it has used mathematics to anticipate a physical event.

What should the results look like?

These are calculated predictions for acrylic with refractive index 1.49 and air with refractive index 1.00.

Internal incidence angle	Predicted refracted angle	Expected observation
20 degrees	About 30.6 degrees	Emerging ray bends away from the normal
30 degrees	About 48.2 degrees	Emerging ray moves nearer the surface
40 degrees	About 73.3 degrees	Emerging ray travels at a shallow angle to the surface
About 42.2 degrees	90 degrees in the ideal model	Critical-angle limit
45 degrees	No propagating refracted ray	Total internal reflection at the flat face

Students can add their measured values in another column and explain differences.

When the Calculator Reveals a Physical Limit

Try calculating the refracted angle for an internal incidence angle of 45 degrees:

sin(r) = 1.49 x sin(45 degrees)

sin(r) = approximately 1.054

But the sine of a real angle cannot exceed 1.

No refracted ray angle satisfies Snell’s law for this arrangement.

This gives total internal reflection a mathematical explanation as well as an observable one.

For interested A-level students, a further subtlety is that an evanescent electromagnetic field extends a short distance beyond the boundary. The elementary ray description concerns the absence of a propagating transmitted beam into the second material.

From the Block to an Optical Fibre

An optical fibre extends this boundary behaviour along a narrow guide.

In a simple step-index fibre:

• The central core has a higher refractive index.
• The surrounding cladding has a lower refractive index.
• Suitable rays meet the core–cladding boundary above the critical angle and remain guided along the core. OpenStax

The material outside the core does not have to be air.

An educational optical-fibre kit or curved acrylic light guide makes a useful follow-up. Couple light into one end and observe the output.

Compare gentle curves with tighter bends, staying within the equipment’s bend limits. Ask students to sketch how changing the guide’s shape could alter the angle at which a ray meets its boundary.

That makes “light travelling round a bend” something they can reason about.

The familiar zigzag diagram is a useful model, particularly for a multimode step-index fibre. More advanced explanations use guided waves and modes.

How does a fibre carry information?

A simple classroom explanation has three stages:

1. A transmitter encodes information by varying light.
2. The fibre guides the optical signal.
3. A receiver detects it.

Real communications systems use more sophisticated encoding than a simple on–off sketch, but the connection with the practical remains powerful.

Also distinguish total internal reflection at a boundary from transmission through a complete system. Absorption, scattering, bends and connections can all reduce the signal.

Five Questions That Reveal Understanding

1. Why does light entering along the normal continue straight?

Its direction is unchanged, although its speed and wavelength can change.

2. Why use a semicircular block?

Radial alignment avoids directional bending at the curved face, isolating the flat boundary being investigated.

3. Can light travelling from air into acrylic undergo total internal reflection at entry?

No. It is travelling towards the higher refractive index material.

4. Is the critical angle 90 degrees?

No. The refracted angle is 90 degrees. The critical angle is the corresponding incidence angle inside the higher-index material.

5. Does reflection only begin above the critical angle?

No. Below it, reflected and transmitted light can both be present.

These questions also expose a limitation of memorising:

sin(c) = 1/n

That shortened expression assumes the second material is approximately air. The general relationship uses both refractive indices.

Make It a Genuine Investigation

Once the basic progression works, students can extend it.

Compare materials. Predict which material should have the smaller critical angle into air, then test the prediction.

Estimate uncertainty. Approach the transition from increasing and decreasing angles. Consider beam width, alignment and protractor resolution.

Test the alignment. Deliberately aim slightly away from the circle’s centre. Explain why extra refraction complicates the experiment.

Create a visual record. Photograph the setup from directly above at several incidence angles.

For my home laboratory and teaching studio, the overhead view is particularly appealing. A sequence of images would let students compare the stages without relying on memory.

Any lines added afterwards should be identified as annotations, especially where they reconstruct an internal path the camera cannot show clearly.

Why I Would Teach This as One Connected Story

Reflection and refraction are often practised as separate sets of diagrams. The critical angle becomes another equation, while optical fibres appear as an application at the end.

I would bring them together around one question:

“What happens if we keep increasing the angle?”

That question gives students a reason to measure, calculate and look again.

Unexpected observations become useful too: a faint reflected ray below the critical angle, an emerging beam that is difficult to locate, or a result that changes when the block slips.

At Hemel Private Tuition, this is the practical approach I value. Observations give the equations meaning, and the equations help students explain what they observe.

Conclusion: A Small Change of Angle, a Bigger Understanding

A transparent block, a narrow beam and a protractor can reveal a complete chain of ideas.

Students establish reflection, measure refraction, predict a critical angle and observe total internal reflection. They can then explain how the same boundary behaviour helps guide light along an optical fibre.

The most valuable outcome is the ability to connect those stages in their own words.

Light meets a boundary. We change the angle. A new question appears.

That is a strong foundation for learning physics: observe carefully, make a prediction, test it and explain the result.

If your child finds GCSE or A-level Physics difficult to connect with, Hemel Private Tuition brings practical observations, mathematical reasoning and exam technique together, in Hemel Hempstead and online.