Refraction Through a Glass Block: O-Level Physics Pin-and-Ray Experiment

where:

• $i$ is the angle of incidence - the angle between the incoming ray and the normal to the surface at the point of entry,
• $r$ is the angle of refraction - the angle between the refracted ray inside the glass and the same normal,
• $n$ is the refractive index of glass relative to air (a dimensionless ratio, always greater than 1 when passing from a less dense to a more dense medium).

The normal is an imaginary line drawn perpendicular to the glass surface at the exact point where the ray enters. Every angle in this experiment is measured from that normal, not from the surface itself.

When light enters glass from air, it slows down and bends toward the normal ($r \lt i$). When it exits glass back into air, it speeds up and bends away from the normal. The refractive index is the same for both interfaces.

For crown glass, $n$ is approximately 1.50. Flint glass has a higher refractive index (around 1.62), and optical fibre glass can reach 1.46–1.55 depending on composition.

2 | Apparatus list

Place the paper on the softboard before you start. Never use graph paper - the printed grid obscures the traced ray lines and makes angle measurement unreliable.

3 | Method

1. Place the glass block on the paper. Centre the block near the middle of the sheet. Hold it firmly and trace around all four edges with a sharp pencil, producing an accurate rectangular outline. Label one long face as the "entry face."
2. Choose the point of incidence. Mark a dot $P$ near the centre of the entry face outline. This is where the incident ray will meet the glass.
3. Draw the normal at $P$. Using a protractor, draw a straight line through $P$ that is exactly 90° to the entry face. Extend this normal at least 5 cm on each side of the face. A freehand normal is the single most common source of error - use the protractor edge against the ruler for a clean perpendicular.
4. Set the angle of incidence. Measure your chosen angle $i$ from the normal and draw a faint pencil line at that angle on the air side of the entry face. This line shows the intended path of the incident ray.
5. Position the first two incident pins. Press pin $A$ into the softboard on the incident ray line, at least 5 cm from $P$. Press pin $B$ between pin $A$ and $P$, also on the incident ray line, at least 5 cm from pin $A$. The two pins must be far apart - pins placed closer than 5 cm together give a poorly defined direction and introduce large angular errors.
6. Place the glass block back on its outline. Align the block precisely with the pencil outline.
7. Sight the two emergent pins on the far side. Look through the exit face of the block from the opposite side. You will see the images of pins $A$ and $B$ through the glass, refracted and laterally displaced. Press pin $C$ into the softboard so that it appears, when viewed through the exit face, to be exactly in line with the images of $A$ and $B$. Press pin $D$
8. Remove the block and pins. Carefully lift the block straight up. You now have four pin-hole marks on the paper: $A$, $B$ (incident side) and $C$, $D$ (emergent side), plus the block outline.
9. Draw the incident and emergent rays. Using a ruler, draw a straight line through holes $A$ and $B$ and extend it to the entry face outline at point $P$. Draw a straight line through holes $C$ and $D$ and extend it back to the exit face outline at point $Q$.
10. Draw the refracted ray inside the block. Join $P$ to $Q$ with a straight line. This is the ray path through the glass.
11. Draw the normal at Q on the exit face and measure the angles there if required. For this experiment, the primary measurements are taken at the entry face.
12. Repeat for at least four further angles of incidence (see Section 5 for the recommended set), drawing a fresh normal each time or using a new sheet of paper for each angle.

4 | Measuring angle of incidence and angle of refraction

Both angles are always measured from the normal, not from the glass surface. This is the most important rule in the entire experiment and the one most frequently violated.

At the entry face (point $P$):

• Angle of incidence $i$: the angle between the incident ray (from the air side) and the normal, measured on the air side of the surface.
• Angle of refraction $r$: the angle between the refracted ray inside the glass (line $PQ$) and the same normal, measured on the glass side.

Place the centre of the protractor exactly at $P$. Align the 0°--180° baseline of the protractor along the normal (not along the surface). Read off the angle between the normal and the incident ray for $i$, and the angle between the normal and the line $PQ$ for $r$.

Why the normal and not the surface? The surface and the normal are exactly 90° apart. If you measure from the surface by mistake, every value will be out by 90°, and $\sin i / \sin r$ will not equal a physically meaningful refractive index. Specifically: $\sin 90° = 1$ regardless of angle, so both your sine values will be near 1 and your ratio near 1, which is the refractive index of air - not glass.

5 | Data table

Use five different angles of incidence, spread across a wide range. Record $i$ and $r$ in whole degrees, then calculate $\sin i$ and $\sin r$ to three decimal places.

The sample data above are consistent with crown glass ($n \approx 1.50$). In a real experiment, your angles of refraction will depend on your specific glass block and the precision of your pin placement.

Column headings must show the quantity name and unit separated by a forward slash, for example "$i$ / °". The sine columns are dimensionless and require no unit.

6 | Graph conventions

Plot $\sin i$ on the y-axis against $\sin r$ on the x-axis.

From Snell's Law, $\sin i = n \sin r$, which has the form $y = mx$. This is a straight line through the origin with gradient equal to $n$. The graph must therefore:

• Pass through the origin (0, 0). Do not offset the axes.
• Have a best-fit straight line drawn with a ruler, not a curve or a dot-to-dot join.
• Have axes labelled with the quantity and the word "sin" written out - for example "sin $i$" with no unit (sine values are dimensionless).
• Spread the plotted points across at least two-thirds of each axis. For five points ranging from $\sin i = 0.34$ to $\sin i = 0.87$, a y-axis from 0 to 1.0 works well.

The gradient is read as:

$$n = \frac{\Delta (\sin i)}{\Delta (\sin r)}$$

Use a large triangle on the best-fit line (not between two plotted data points) and pick coordinates to three decimal places. The larger the triangle, the smaller the reading error.

For a comprehensive walkthrough of graph conventions - scale selection, best-fit lines, gradient triangles, and intercept reading - see the O-Level Physics Graphing and Linearisation Clinic.

7 | Worked example

Using the sample data from Section 5, calculate $n$ from the gradient of the best-fit line.

From the data, take two well-separated points on the best-fit line (not actual data points):

• Point 1: $\sin r = 0.20$, $\sin i = 0.304$
• Point 2: $\sin r = 0.55$, $\sin i = 0.831$

$$n = \frac{0.831 - 0.304}{0.55 - 0.20} = \frac{0.527}{0.35} = 1.506$$

Round to three significant figures and report as $n = 1.51$.

You can cross-check by averaging the individual $\sin i / \sin r$ ratios from the table:

$$n_\text{avg} = \frac{1.52 + 1.53 + 1.52 + 1.49 + 1.51}{5} = \frac{7.57}{5} = 1.51$$

Both methods agree, which is reassuring. However, the graph gradient is the accepted method for Paper 3 because it uses all five data points simultaneously, reducing the impact of any single measurement error.

The accepted value for crown glass is 1.50, so this result is within 0.7 % of the standard - well within the range of experimental uncertainty from pin placement.

8 | Five mark-losing mistakes

Mistake 1 - Drawing the normal freehand

A freehand normal is almost never exactly 90° to the surface. Even a 2° error in the normal shifts both $i$ and $r$ by 2°, producing sine values that are consistently wrong. The error is systematic - it affects every angle in the same direction - so the gradient of your graph is skewed. Always construct the normal with a protractor held firmly against a ruler.

Mistake 2 - Placing the pins less than 5 cm apart

If pins $A$ and $B$ are only 1–2 cm apart, the line joining them is sensitive to any lateral displacement of either pin. A 0.5 mm placement error becomes a 1.4° directional error when the pins are 2 cm apart, but only a 0.3° error when they are 10 cm apart. Keep all pairs of pins at least 5 cm - and ideally 8–10 cm - apart.

Mistake 3 - Measuring the angle from the block edge (surface)

This is addressed in Section 4, but it is worth repeating here because it is the error examiners see most often. The angle of incidence is measured from the normal. The surface and the normal are 90° apart, so every misread angle is wrong by 90°. If your measured $r$ is larger than your measured $i$, you have very likely measured from the surface.

Mistake 4 - Joining data points dot-to-dot instead of drawing a best-fit line

A dot-to-dot graph is not a graph of the physics - it is a map of your measurement errors. The best-fit straight line minimises the combined deviation of all points and represents the underlying relationship. In Paper 3 marking schemes, a dot-to-dot "line" scores zero for the graph line mark, regardless of how accurately the points are plotted.

Mistake 5 - Quoting $n$ as "1.5" instead of "1.50"

The O-Level Physics mark scheme distinguishes between significant figures. A refractive index of "1.5" has two significant figures. Given that you have collected five data points and calculated a gradient to three significant figures, quoting only two significant figures implies lower precision than your data support. Examiners expect the result to be given as "1.50" (three significant figures) - the trailing zero is not optional.

9 | Paper 3 planning-question variant

Paper 3 occasionally presents this experiment as a planning question rather than a standard practical. A typical prompt reads:

"A student has access to a rectangular block made of transparent plastic and a set of optical pins. Design an experiment to determine whether the plastic has the same refractive index as crown glass ($n = 1.50$)."

Structure your answer around these headings:

1. Aim: Determine the refractive index of the plastic block and compare it with 1.50.
2. Independent variable: Angle of incidence $i$, varied over the range 20° to 60° in steps of 10°.
3. Dependent variable: Angle of refraction $r$, measured from the normal inside the plastic.
4. Control variables: Use the same block throughout. Keep the entry face the same for all readings. Keep the room temperature constant (temperature affects the density of the material and therefore $n$ very slightly).
5. Method outline: Trace the block outline, draw normals, use four pins per reading (two incident, two emergent), measure $i$ and $r$ with a protractor, tabulate $i$, $r$, $\sin i$, $\sin r$, plot $\sin i$ against $\sin r$, and find the gradient.
6. Results processing: If the gradient equals 1.50 (within experimental uncertainty), conclude that the plastic has the same refractive index as crown glass. If the gradient differs significantly - for example 1.65 - conclude that it does not.
7. Sources of error: Freehand normal, pins too close together, parallax when reading the protractor.
8. Safety: No significant hazards. Optical pins are sharp - handle with care; do not press them in with excessive force.

For a detailed breakdown of planning-question structure and mark allocation, pair this section with the O-Level Physics Paper 3 Marking Micro-Habits guide.

10 | Apparatus troubleshooting

Ghost images (multiple pin images visible)

When you look through the exit face of the glass block, you may see two or more faint images of the incident pins rather than one clear image. Ghost images arise from multiple internal reflections within the block - light bouncing between the top and bottom faces before exiting. They are most pronounced when the block is thick or the glass surface is not perfectly flat.

To deal with ghost images: identify the brightest central image (this is the directly refracted ray) and align pins $C$ and $D$ with it. Ignore the fainter peripheral images. If the block surface has scratches, position the entry point $P$ on an undamaged section.

Pin shadows

At certain angles, the base of a pin casts a shadow onto the paper behind the block. If pin $C$ or $D$ falls in this shadow zone, the mark left by the pin after removal is hard to locate precisely. To avoid this, tilt the desk lamp to the side so shadows fall away from the observation zone. Keep the lamp at the same position throughout all readings so shadow patterns are consistent.

Block warmth distorting rays

If a desk lamp is placed very close to the block for extended periods, the glass heats unevenly. Glass that is warmer has a marginally lower refractive index than cold glass. Over a long session with many angle repeats, this could introduce a small systematic drift in your refraction angles. Keep the lamp at least 30 cm from the block and allow the block to return to room temperature between readings if you notice the emerging ray shifting without any change in $i$.

11 | Where this fits

The refraction glass block experiment sits at the intersection of three skill areas tested in Paper 3:

• Ray-tracing accuracy - constructing normals, placing pins, and connecting marked points.
• Graph work - linearising Snell's Law, plotting through the origin, and reading a gradient.
• Significant figures and units - reporting $n$ correctly and labelling table columns properly.

Practise each skill separately before combining them in a timed sit:

• For graph-plotting conventions, gradient reading, and linearisation of non-linear relationships, see the O-Level Physics Graphing and Linearisation Clinic.
• For the full set of Paper 3 marking habits - significant figures, table formats, error statements - see O-Level Physics Paper 3 Marking Micro-Habits.
• For the companion optics experiment (finding focal length with a converging lens), see the Lens Focal Length Experiment.
• For uncertainty estimation and decimal place conventions, see the O-Level Physics Error and Uncertainty Masterclass.

Sources

• SEAB 2026 O-Level Physics syllabus (6091): https://www.seab.gov.sg/docs/default-source/national-examinations/syllabus/2026/2026-o-level-syllabus/6091_y26_sy.pdf
• O-Level Physics Experiments hub - full index of Paper 3 experiment walkthroughs.
• O-Level Physics Optics Practical Handbook - ray diagrams, reflection, refraction, and total internal reflection.

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