Interactive practical

Measuring refractive index

Rotate a ray box around a semicircular block, read refraction angles on the protractor, then find the refractive index from a graph of sin i against sin r and check it against the critical angle.

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A-Level Physics

Measuring refractive index

CCEA 1210 — matched to your course.

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Practical focus

Measure incidence and refraction angles and determine refractive index from Snell's law.

Practical method

Aim

Determine the refractive index of glass from angles of incidence and refraction (Snell's law) and from the critical angle.

Variables

Independent variable: angle of incidence i
Dependent variable: angle of refraction r
Control variables: the same glass block; narrow ray from one source.

Apparatus

Rectangular and semicircular glass blocks
Ray box with narrow slit
Protractor
Sharp pencil and paper
Ruler

Method

Trace the rectangular block and draw a normal. Shine a narrow ray at angles of incidence from 20° to 60°.
Mark the emerging ray, remove the block and draw the ray inside the glass; measure r.
Plot sin i against sin r: Snell's law gives a straight line through the origin with gradient n.
Critical angle: shine the ray through the curved face of a semicircular block towards the centre of the flat face.
Increase the angle until the refracted ray just grazes the surface; this angle is the critical angle c, and n = \(\dfrac{1}{\sin c}\).

Sample results

Rectangular glass block.

i / °	r / °	sin i	sin r
20	13.2	0.342	0.228
30	19.5	0.500	0.334
40	25.4	0.643	0.429
50	30.7	0.766	0.511
60	35.3	0.866	0.578

Analysis

sin i against sin r is a straight line through the origin with gradient 1.50, so n = 1.50. The critical angle measured with the semicircular block is 42°, giving n = \(\dfrac{1}{\sin 42^{\circ}}\) = 1.49, in agreement.

Uncertainty

Angles are read to ±1°. At r ≈ 13° this is about 8% in sin r, but at r ≈ 35° only about 2.5%, so larger angles are more reliable. Using the gradient of the graph reduces the effect of individual errors.

Errors and improvements

Problem	Effect	Improvement
Wide ray	Angles hard to measure	Use a narrow slit and mark the ray centre
Normal drawn inaccurately	All angles wrong	Draw the normal with a protractor
Critical angle judged at the wrong point	c uncertain	Find where the refracted ray just disappears and average approaches

Risk assessment

Hazard	Risk	Control measure
Hot ray box	Burns	Do not touch the housing
Glass block	Cuts if chipped or dropped	Handle carefully

Common mistakes

Measuring angles from the surface instead of the normal.
Plotting i against r instead of sin i against sin r.
Using n = sin c instead of n = \(\dfrac{1}{\sin c}\).

Worked analysis

At i = 50°, r = 30.7°: n = \(\dfrac{\sin 50^{\circ}}{\sin 30.7^{\circ}}\) = \(\dfrac{0.766}{0.511}\) = 1.50. Critical angle: sin c = \(\dfrac{1}{1.50}\), so c = 41.8°.

Common misconception

Total internal reflection needs light travelling from the denser medium (glass) towards the less dense medium (air), at more than the critical angle.

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