Describe an experiment to show refraction of light by transparent blocks of different shapes
3.2.2 Refraction of Light
Objective
To describe, set up and analyse an experiment that demonstrates the refraction of light when it passes through transparent blocks of different shapes (a rectangular slab and a triangular prism). The experiment will also be used to determine the refractive index of the material and to investigate the critical angle and total internal reflection.
Key Definitions
Normal – a line drawn perpendicular to a surface at the point of incidence.
Angle of incidence \(i\) – angle between the incident ray and the normal.
Angle of refraction \(r\) – angle between the refracted ray inside the new medium and the normal.
Angle of emergence \(e\) – angle between the emergent ray (after leaving the block) and the normal to the exit face.
Prism angle \(A\) – the apex angle of a triangular prism (the angle between the two refracting faces).
Deviation \(\delta\) – the total change in direction of the emergent ray, \(\delta = i+e-A\).
Critical angle \(c\) – the smallest angle of incidence in the denser medium for which the refracted ray travels along the interface (\(r=90^{\circ}\)). For \(i>c\) total internal reflection occurs.
Lateral shift \(d\) – the parallel displacement of a ray after passing through a slab with parallel faces, \(d = t\tan(i-r)\) where \(t\) is the slab thickness.
Theoretical Background (concise)
- When light passes from one transparent medium to another its speed changes, causing the ray to bend – this is refraction.
- Snell’s law relates the angles of incidence and refraction:
\(n{1}\sin i = n{2}\sin r\)
In the laboratory air can be taken as \(n_{1}\approx1\); therefore the refractive index of the block material is
\(n = \dfrac{\sin i}{\sin r}\)
- Rectangular slab (parallel faces) – the emergent ray is parallel to the incident ray (\(i=e\)). The ray is displaced laterally by
\(d = t\tan(i-r)\)
- Triangular prism (non‑parallel faces) – the emergent ray is deviated. The deviation is
\(\delta = i+e-A\)
where \(A\) is the measured prism angle.
- Critical angle for light travelling from a denser medium (refractive index \(n\)) to air is
\(c = \sin^{-1}\!\left(\dfrac{1}{n}\right)\)
Example: for typical crown glass \(n\approx1.50\), \(c = \sin^{-1}(1/1.50)=41.8^{\circ}\).
Apparatus
| Item | Purpose |
|---|---|
| Ray box (or low‑power laser pointer, ≤ 5 mW) | Produces a narrow, straight light beam |
| Transparent rectangular slab (glass or Perspex, thickness ≈ 5 mm) | Shows refraction at two parallel faces and lateral shift |
| Transparent triangular prism (equilateral or isosceles, apex angle ≈ 60°) | Shows refraction at non‑parallel faces and deviation |
| Protractor or graduated rotating platform | Sets and measures the angle of incidence accurately |
| White sheet of A4 paper | Background on which the ray is traced |
| Ruler (0‑30 cm) or measuring scale | Measures lateral shift \(d\) and prism angle \(A\) |
| Pencil and eraser | Mark incident, refracted and emergent rays |
Experimental Setup
- Secure a white sheet of paper on a flat table.
- Place the ray box so that the emerging beam strikes the paper near its centre.
- Mount the transparent block on a rotating platform or on a base that has a protractor fixed to it. The platform must allow the block to be turned through a range of incidence angles while keeping the beam centred on the paper.
- Draw the normal to the relevant face of the block with a ruler and a pencil.
- For each trial, mark on the paper:
- the incident ray (extension of the beam before it meets the block),
- the point of entry,
- the refracted ray inside the block,
- the point of exit, and
- the emergent ray.
Procedure
- Normal incidence check – set the beam to strike the block at \(i=0^{\circ}\). Verify that the ray continues in a straight line (no deviation, no shift).
- Rectangular slab
- Rotate the slab to give incidence angles of 10°, 20°, 30°, 40° (or any convenient equal steps).
- For each angle record:
- \(i\) (read from the protractor),
- \(r\) (measure with a protractor on the paper),
- \(e\) (should equal \(i\) for a slab),
- lateral shift \(d\) (distance between the incident and emergent rays measured with the ruler).
- Calculate the theoretical shift using \(d_{\text{calc}} = t\tan(i-r)\) (with \(t\) = slab thickness) and compare with the measured value.
- Triangular prism
- Measure the prism apex angle \(A\) with a protractor before starting the trial.
- Set incidence angles (same values as for the slab). For each angle record \(i\), \(r\), \(e\) and compute the deviation \(\delta = i+e-A\).
- Critical‑angle investigation (optional)
- Replace the prism with a high‑index glass prism (e.g. \(n\approx1.70\)).
- Increase the angle of incidence inside the glass until the emergent ray disappears and the beam is reflected back inside the prism – this is total internal reflection.
- Compare the observed angle with the calculated critical angle \(c = \sin^{-1}(1/n)\).
Data Tables
Rectangular slab
| i (°) | r (°) | e (°) | d (mm) – measured | d (mm) – calculated | n = sin i / sin r |
|---|---|---|---|---|---|
| 10 | |||||
| 20 | |||||
| 30 | |||||
| 40 |
Triangular prism
| i (°) | r (°) | e (°) | δ (°) | n = sin i / sin r |
|---|---|---|---|---|
| 10 | ||||
| 20 | ||||
| 30 | ||||
| 40 |
Data Analysis
- Refractive index from Snell’s law – For each trial calculate \(n = \dfrac{\sin i}{\sin r}\). Plot \(\sin i\) (y‑axis) against \(\sin r\) (x‑axis). The gradient of the straight‑line fit gives the refractive index of the material (since \(n_{\text{air}}\approx1\)). Include error bars and determine the uncertainty in the gradient.
- Rectangular slab
- Check that \(i = e\) within experimental error, confirming that parallel faces produce a parallel emergent ray.
- Compare measured and calculated lateral shifts. Use the agreement (or discrepancy) to comment on experimental uncertainties (e.g. parallax, thickness measurement).
- Triangular prism
- Verify the deviation formula \(\delta = i+e-A\) by substituting the measured values.
- From the \(\sin i\) vs \(\sin r\) graph obtain a second estimate of \(n\) and compare with the slab result.
- Critical angle
- Calculate the theoretical critical angle for the prism material and compare with the angle at which total internal reflection was first observed.
- Discuss why the phenomenon is important for optical fibres and prisms in binoculars.
Conclusion
The experiment confirms that light changes direction whenever it passes from one transparent medium to another. A rectangular slab with parallel faces produces a lateral shift but leaves the emergent ray parallel to the incident ray, whereas a triangular prism causes a measurable deviation that depends on the prism angle and the refractive index. By applying Snell’s law to the measured angles, the refractive index of the material can be determined. The critical‑angle part demonstrates total internal reflection, a principle that underlies many modern optical devices.
Safety Precautions
- Never look directly into the ray box or laser source. Keep the beam below eye level.
- Use a low‑power laser (≤ 5 mW) or a ray box with a diffuser to minimise eye hazard.
- Never point the beam at anyone’s eyes or reflective surfaces.
- Handle glass prisms with both hands; support them on all sides to avoid breakage.
- Secure the paper to the table (e.g. with tape) so it does not shift during measurements.
- Turn off the laser/ray box when the apparatus is not in use.
Extension Activities
- Refractive‑index determination – Using the \(\sin i\) vs \(\sin r\) graph, calculate the gradient and its uncertainty. Compare the result with the known value for the material (glass ≈ 1.50, Perspex ≈ 1.49).
- Dispersion – Replace the laser with a white‑light source and a coloured filter or a diffraction grating. Observe how different colours are refracted by different amounts (higher \(n\) for shorter wavelengths).
- Critical‑angle experiment – Use prisms made from different glasses (e.g. crown glass, flint glass) and calculate their critical angles. Demonstrate total internal reflection for each.
- Real‑world applications – Discuss how the principles observed are used in optical fibres, periscopes, camera lenses, and the design of binocular prisms.