IGCSE CP5 – Refractive Index | Edexcel International GCSE Physics

Theory — Refractive Index

The refractive index n tells you how much a material bends light. It can be determined experimentally from a graph of sin θᵢ against sin θᵣ.

Snell's Law

When light passes from air into glass, Snell's Law relates the angle of incidence θᵢ and the angle of refraction θᵣ — both measured from the normal:

n₁ sin θᵢ = n₂ sin θᵣ Since n₁ = 1.00 (air): sin θᵢ = n × sin θᵣ

n = refractive index of glass · θᵢ = angle of incidence · θᵣ = angle of refraction

Rearranging: n = sin θᵢ / sin θᵣ

Why Plot a Graph?

Calculating n from a single pair of angles is unreliable — one measurement could have a large error. Instead, take readings at many different angles and plot a graph:

sin θᵢ = n × sin θᵣ → Plot sin θᵢ (y-axis) against sin θᵣ (x-axis)

This is of the form y = mx. Straight line through origin. Gradient = n. Using the gradient gives a much more reliable value of n than any single reading.

What the Graph Tells You

Straight line through origin — confirms Snell's Law: sin θᵢ ∝ sin θᵣ
Gradient = n — the refractive index of the glass
n > 1 always — glass is optically denser than air, so θᵣ < θᵢ, so sin θᵢ > sin θᵣ, so gradient > 1
Scatter of points — shows random errors in angle measurement; best-fit line averages these out

Procedure

Taking systematic readings of θᵢ and θᵣ to plot sin θᵢ vs sin θᵣ and find n from the gradient.

Equipment

Rectangular glass block · Ray box · Plain white paper · Sharp pencil · Ruler · Protractor · Calculator

1

Set up the glass block and draw the normal

Place the glass block on paper, outline it. Choose your entry point on the top surface. Draw the normal — a vertical line perpendicular to the top surface at that point.

💡 Draw the normal before you start. Every angle measurement in this experiment is made from the normal — not from the surface.

2

Set angle of incidence to 10°

Direct the ray box so the ray hits the entry point at θᵢ = 10° from the normal. Mark the incident ray with two dots. Mark the emergent ray below the block with two dots.

💡 Use small angles first. At large angles (above 60°) the refracted ray inside the glass becomes dim and hard to see accurately.

3

Measure θᵣ

Remove the block. Draw the full ray path. At the entry point, place the protractor centre on the entry point with the baseline along the normal. Measure θᵣ — the angle between the refracted ray (inside glass) and the normal.

4

Repeat for 6–8 angles

Repeat for θᵢ = 20°, 30°, 40°, 50°, 60°. For each: mark the rays, measure θᵣ, calculate sin θᵢ and sin θᵣ (to 3 decimal places).

💡 Use a new sheet of paper for each angle, or carefully label each ray. Do not try to draw all rays on one sheet — it becomes unreadable.

5

Plot sin θᵢ vs sin θᵣ

Plot sin θᵢ on the y-axis and sin θᵣ on the x-axis. Draw the best-fit straight line through the origin. The gradient = n.

💡 The line must pass through the origin — when θᵢ = 0 (ray along normal), θᵣ = 0 and sin 0 = 0. If your best-fit line misses the origin, check for systematic error in your angle measurements.

      🔦 Set the angle of incidence, read θᵣ from the display, then ✚ Record Reading. Take 6–8 readings across 10°–60° then check the Graph tab.
    

Angle of Incidence

θᵢ from normal 30°

10°60°

Current Reading

θᵢ (incidence)30°

θᵣ (refraction)—

sin θᵢ—

sin θᵣ—

n = sinθᵢ/sinθᵣ—

Readings recorded: 0 / 6 target

Data Table

sin θᵢ (y-axis) plotted against sin θᵣ (x-axis) gives a straight line through the origin. Gradient = n.

#	θᵢ / °	θᵣ / °	sin θᵢ (3 d.p.)	sin θᵣ (3 d.p.)	n = sinθᵢ/sinθᵣ
No readings yet — use the Simulation tab.

Graph — sin θᵢ vs sin θᵣ

Straight line through origin confirms Snell's Law. Gradient = refractive index n.

Refractive index n

— from graph gradient

Graph results

Gradient (= n)—

y-intercept (→ 0)—

R²—

True n (glass)1.500

% error—

Interpretation

Record at least 5 readings to see analysis.

Questions

Question 1

A student measures θᵢ = 40° and θᵣ = 25° for a glass block. Calculate the refractive index n. Why is it better to use the gradient of the sin θᵢ vs sin θᵣ graph rather than this single pair of values?

n = sin θᵢ / sin θᵣ = sin 40° / sin 25° = 0.6428 / 0.4226 = 1.52. Using a single pair of values is unreliable because: (1) any error in measuring either angle is magnified in the calculation; (2) the protractor can only be read to ±0.5°, giving a possible percentage error of several percent at small angles. The graph gradient uses all readings simultaneously — random errors in individual readings cancel out when drawing the best-fit line, giving a more reliable value of n. The straight line through the origin also confirms that Snell's Law holds across all angles tested.

Question 2

Explain why the graph of sin θᵢ against sin θᵣ must pass through the origin, and what it would mean if it did not.

When θᵢ = 0° (ray hits along the normal), no refraction occurs — the ray passes straight through. So θᵣ = 0° and sin θᵣ = 0. Since sin θᵢ = n × sin θᵣ = n × 0 = 0, both axes are zero at this point, so the line passes through the origin. If the line does not pass through the origin, this indicates a systematic error — most likely that the normal was drawn incorrectly (not perpendicular to the surface), causing all angles to be measured from a wrong reference line. This shifts all readings by a fixed amount, displacing the line from the origin.

Question 3

A student's sin θᵢ vs sin θᵣ graph has a gradient of 1.62. The accepted value for the glass block is n = 1.50. Calculate the percentage error and suggest two reasons why the student's value might be higher than expected.

% error = |1.62 − 1.50| / 1.50 × 100 = 0.12/1.50 × 100 = 8.0%. Reasons for the higher value: (1) The normal may not have been drawn accurately perpendicular to the surface — if the normal is tilted, all angles of refraction will appear smaller than they really are, making sin θᵣ smaller and the ratio sin θᵢ/sin θᵣ larger. (2) Parallax error when marking the ray dots — if the pencil is not held vertically when marking dots on the paper, the ray appears at a slightly different position, leading to errors in the traced angle. (3) The glass block may have moved slightly between taking the reading and tracing the ray, altering the geometry.