Investigating Refraction and Critical Angle with a Semicircular Block

Refraction is one of the most important topics in GCSE and A Level Physics. A simple semicircular acrylic block, a ray box, and a protractor create one of the clearest experiments for observing how light bends, how angles relate to each other, and where total internal reflection begins.

This investigation connects the theory of refractive index with hands-on measurements and gives students real data to support Snell’s Law.

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Why Use a Semicircular Block?

The semicircle has a special advantage:
If the light ray enters through the curved surface, it always hits the flat surface at a right angle, meaning no refraction occurs at entry.

This ensures all bending happens at the flat face, simplifying measurements and removing unnecessary complications.

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The Experiment

Equipment:

• Semicircular Perspex or glass block

• Ray box with single-slit attachment

• Protractor or printed angle sheet

• A3 paper and pencil

• Ruler

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1. Investigating Refraction (Snell’s Law)

1. Place the block on paper and draw around it.

2. Shine a narrow ray into the curved surface so it reaches the flat side at different angles of incidence.

3. Mark the incident ray, refracted ray, and normal.

4. Measure:

   • Angle of incidence $i$

   • Angle of refraction $r$

5. Plot a graph of $\sin i$ against $\sin r$.

The gradient of the straight-line graph gives the refractive index of the block.

Typical value for Perspex: 1.49.

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2. Investigating Critical Angle and Total Internal Reflection

1. Keep the light ray inside the block and slowly increase the angle of incidence at the flat face.

2. Observe:

   • At small angles → refraction out of the block

   • At a specific angle → refracted ray emerges at 90°

   • Beyond that → the ray reflects back internally

That angle where the refracted ray is at 90° is the critical angle $c$.

From measurements:

$$\sin c = \frac{1}{n}$$

For Perspex

$$c \approx 42^\circ$$

Students can test this experimentally and compare to theory.

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What Students Learn

• Light changes speed when entering a new medium

• Snell’s Law links angles and refractive index

• Total internal reflection occurs beyond the critical angle

• Semicircular blocks make the geometry clean and accurate

They also gain practice drawing diagrams, measuring angles, and producing graphs — essential skills for GCSE and A Level exams.

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Skills Highlight

• Accurate angle measurement

• Collecting data for $\sin i$ vs $\sin r$

• Calculating refractive index

• Identifying the critical angle

• Understanding when and why total internal reflection happens

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Why It Works in Teaching

The experiment is fast, visual, and precise. Students see the ray bend in real time, compare theory with measurement, and consolidate one of the most important optical concepts in physics — with equipment found in every school lab.