Refraction of Light (Senior 3 Physics): free lessons | Ganzaa

Refraction of Light

Lessons

Senior 3 · Physics

Refraction of Light

5 lessons

Lesson 1 of 5

Refraction, Refractive Index and the Laws of Refraction

30 min

The coin that comes back

Put a coin flat on the bottom of an empty mug or tin. Move your head back until the rim just hides the coin, and then keep your head perfectly still while a friend pours water slowly into the mug, taking care not to move the coin. The coin comes back into view. Neither the coin nor your eye moved: the light from the coin changed direction as it left the water, and so it now clears the rim and reaches your eye.

In S1 you learned that light travels in straight lines and how it reflects from a plane mirror, and in S2 you located images in curved mirrors. This unit follows light as it crosses from one transparent material into another. That bending explains the coin, the shallow look of clear water, optical fibres, lenses in spectacles and cameras, and the colours of a rainbow.

Definition

Refraction: the change in direction of light as it passes at an angle from one transparent medium into another, caused by a change in its speed. Example: a ray passing from air into glass.

Medium (plural media): the material light travels through, such as air, water or glass.

Normal: a line drawn at 90° to the boundary at the point where the ray meets it. All angles in refraction are measured from the normal, never from the surface.

Angle of incidence $i$ : the angle between the incident ray and the normal. Angle of refraction $r$ : the angle between the refracted ray and the normal.

Optically denser medium: the medium in which light travels more slowly (glass is optically denser than air).

Experiment: tracing a ray through a glass block

Apparatus: a rectangular glass or Perspex block, a sheet of white paper on a soft board, a ray box with a single slit (or four optical pins), a protractor, a ruler and a sharp pencil.

Place the block in the middle of the paper and draw round it. Mark a point P on the top edge and draw the normal through P with the protractor.
Draw a line meeting P at an angle of incidence of 20° to the normal.
Shine the narrow ray along this line (or put two pins on it). Mark where the ray leaves the far side of the block (or look through the block and place two more pins in line with the images of the first two).
Remove the block and join the points to show the ray's path through the glass. Measure the angle of refraction $r$ at P.
Repeat for $i = 30^\circ, 40^\circ, 50^\circ$ and $60^\circ$ , and work out $\frac{\sin i}{\sin r}$ each time.

The figure shows one trace. On entering the glass, the ray bends towards the normal ( $r = 31^\circ$ is smaller than $i = 50^\circ$ ). On leaving, it bends away from the normal and comes out at $e = 50^\circ$ .

$i$	$r$ (measured)	$\sin i$	$\sin r$	$\frac{\sin i}{\sin r}$
20°	13°	0.342	0.225	1.52
30°	19°	0.500	0.326	1.54
40°	25°	0.643	0.423	1.52
50°	31°	0.766	0.515	1.49
60°	35°	0.866	0.574	1.51

These are illustrative results for one glass block. The angle of refraction grows as $i$ grows, but not in proportion. The ratio $\frac{\sin i}{\sin r}$ , however, stays close to 1.5 every time; the small spread comes from measuring angles to the nearest degree. Their mean, 1.52, is the refractive index of this glass.

Warning

Safety: laser pointers and your eyes. Some schools use a laser pointer instead of a ray box. The eye focuses a laser beam onto a tiny spot on the retina. Even a genuine low-power beam can dazzle and leave after-images, and pointers sold as low-power are sometimes far stronger than their label says; such pointers have caused permanent eye injuries, especially to children.

Use only a pointer marked Class 1 or Class 2 (below 1 mW), and only with your teacher present.
Never look into the beam, and never point it at a person, an animal, a driver or an aircraft.
Keep the beam flat on the bench, below everyone's eye level. The faces of the glass block reflect part of the beam, so check where the reflections go.
If a beam enters someone's eye, stop and tell the teacher. If their sight is still blurred, or they see a dark or bright spot, they must have the eye examined at a health centre promptly.

Handle the glass block with care too: a chipped edge is sharp.

The laws of refraction

Experiments like this one, repeated for many materials, give two laws.

First law: the incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
Second law (Snell's law): for light passing between two given media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.

When light passes from air (strictly, a vacuum) into a medium, that constant is the medium's refractive index $n$ :

n = \frac{\sin i}{\sin r}

The law is named after the Dutch scientist Willebrord Snellius, who found it in 1621.

Why light bends: a change of speed

Light travels at $c = 3.00 \times 10^{8}\,\mathrm{m\,s^{-1}}$ in a vacuum (and almost as fast in air) but more slowly in water and glass. Think of a toy car rolling at an angle off a smooth floor onto a carpet. The wheel that reaches the carpet first slows down first, while the other wheel is still fast, so the car swings round towards the normal. Light entering glass at an angle turns for the same reason. The refractive index compares the two speeds:

n = \frac{c}{v} = \frac{\text{speed of light in a vacuum}}{\text{speed of light in the medium}}

Medium	Refractive index $n$	Speed of light $v$ (m s⁻¹)
Air	1.0003 (use 1.00)	$3.00 \times 10^{8}$
Ice	1.31	$2.29 \times 10^{8}$
Water	1.33	$2.26 \times 10^{8}$
Crown glass	1.52	$1.97 \times 10^{8}$
Flint glass	1.66	$1.81 \times 10^{8}$
Diamond	2.42	$1.24 \times 10^{8}$

Values are for yellow light. Three rules follow:

Into an optically denser medium (light slows down): the ray bends towards the normal, so $r \lt i$ .
Into an optically less dense medium (light speeds up): the ray bends away from the normal.
Along the normal ( $i = 0^\circ$ ): the light slows down but does not change direction.

Definition

Refractive index $n$ of a medium: the ratio of the speed of light in a vacuum to its speed in the medium, $n = \frac{c}{v}$ ; equal to $\frac{\sin i}{\sin r}$ for light entering the medium from air. It is a ratio, so it has no unit, and it is never less than 1. Example: for water, $n = 1.33$ .

Worked example 1: finding a refractive index

A ray in air strikes a plastic block at an angle of incidence of 40°. The angle of refraction is 25°. Find the refractive index of the plastic.

n = \frac{\sin i}{\sin r} = \frac{\sin 40^\circ}{\sin 25^\circ} = \frac{0.643}{0.423} = 1.52

Set your calculator to degrees (D or DEG) before you start.

Worked example 2: finding an angle of refraction

Light in air strikes the surface of water ( $n = 1.33$ ) at an angle of incidence of 50°. Find the angle of refraction.

\sin r = \frac{\sin i}{n} = \frac{\sin 50^\circ}{1.33} = \frac{0.766}{1.33} = 0.576

r = \sin^{-1}(0.576) = 35.2^\circ \approx 35^\circ

Check: $r \lt i$ , as it must be for light entering a denser medium.

Worked example 3: speed of light in diamond

Diamond has refractive index 2.42. Find the speed of light in diamond.

v = \frac{c}{n} = \frac{3.00 \times 10^{8}}{2.42} = 1.24 \times 10^{8}\,\mathrm{m\,s^{-1}}

Light leaving a denser medium

A light path can always be reversed: if light goes from air to glass along a path, it can go back along the same path. So for light passing from a medium of index $n$ into air, with angle $\theta_m$ in the medium and $\theta_a$ in air:

\sin \theta_a = n \sin \theta_m

Both forms are special cases of the general rule $n_1 \sin \theta_1 = n_2 \sin \theta_2$ , where each angle is measured from the normal in its own medium.

Through a parallel-sided block

Look again at the block in the figure. At the top face the ray refracts from 50° to 31°. Because the two faces are parallel, it meets the bottom face at 31° too, and leaving the glass reverses the first refraction, so it comes out at 50°. The emergent ray is parallel to the incident ray, but shifted sideways by a distance $d$ , the lateral displacement. The displacement is larger for a thicker block, a larger angle of incidence and a higher refractive index. A ray striking the block along the normal passes straight through with no displacement at all.

Worked example 4: from water into air

A ray inside a pond meets the surface at 30° to the normal. Find the angle at which it enters the air ( $n_{\text{water}} = 1.33$ ).

\sin \theta_a = n \sin \theta_m = 1.33 \times \sin 30^\circ = 1.33 \times 0.500 = 0.665

\theta_a = \sin^{-1}(0.665) = 41.7^\circ

The ray bends away from the normal, from 30° to 41.7°. (Try the same sum with 60° inside the water: $1.33 \times 0.866 = 1.15$ , and no angle has a sine bigger than 1. Lesson 2 explains what the light does then.)

Real and apparent depth

Back to the coin. Rays from the coin bend away from the normal as they leave the water. Your eye and brain assume light travels in straight lines, so they trace the rays back to a point $I$ above the coin. The coin seems nearer the surface than it is.

For viewing from almost directly above,

n = \frac{\text{real depth}}{\text{apparent depth}}

This is why a clear stream or pool looks shallower than it really is. Before you wade or jump into clear water, check its depth with a stick: never judge it by eye. Someone trying to spear a fish must aim below where the fish appears to be.

Worked example 5: a clear water tank

The water in a tank is 1.20 m deep. How deep does it look from directly above ( $n = 1.33$ )?

\text{apparent depth} = \frac{\text{real depth}}{n} = \frac{1.20}{1.33} = 0.902\,\mathrm{m} \approx 0.90\,\mathrm{m}

The bottom seems to be raised by about 0.30 m.

Worked example 6: measuring n with a pencil mark

A cross drawn on paper is viewed from above through a glass block 6.0 cm thick. A pin moved to the same apparent position is 4.0 cm below the top of the block. Find the refractive index of the glass.

n = \frac{\text{real depth}}{\text{apparent depth}} = \frac{6.0}{4.0} = 1.5

Warning

Common mistakes

Measuring the angle from the surface instead of from the normal. If a ray makes 60° with the surface, then $i = 30^\circ$ .
Dividing the angles, $\frac{i}{r}$ , instead of their sines, $\frac{\sin i}{\sin r}$ .
Leaving the calculator in radians: $\sin 30$ must give 0.5.
Giving $n$ a unit, or a value below 1. If you get $n \lt 1$ , you have swapped $i$ and $r$ .

Tip

Slow down, swing in. Think of the toy car: when light slows down (into glass or water) it swings in towards the normal; when it speeds up (out into air) it swings away. The bigger the refractive index, the slower the light and the sharper the turn.

Snell's Law (Refraction), by the physics teacher Kit Betts-Masters. Watch how the angles are measured from the normal, and how the ratio of the sines is used to find a refractive index.

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Practice

State the two laws of refraction.
A ray in air strikes a glass block at an angle of incidence of 35°, and the angle of refraction is 22°. Find the refractive index of the glass.
Light in air strikes water ( $n = 1.33$ ) at an angle of incidence of 60°. Find the angle of refraction.
Find the speed of light in crown glass, $n = 1.52$ .
Light travels at $2.25 \times 10^{8}\,\mathrm{m\,s^{-1}}$ in a liquid. Find the refractive index of the liquid.
A small stone lies 0.80 m below the surface of clear water ( $n = 1.33$ ). How deep does it appear when viewed from directly above?
A ray inside a glass block ( $n = 1.50$ ) meets the glass-to-air surface at 30° to the normal. Find the angle it makes with the normal in air.
Explain why the ray leaving a parallel-sided glass block is parallel to the ray that entered it. What happens to a ray that strikes the block along the normal?

Show answersHide answers

(1) The incident ray, refracted ray and normal at the point of incidence lie in one plane. (2) For two given media, $\frac{\sin i}{\sin r}$ is a constant (Snell's law).
$n = \frac{\sin 35^\circ}{\sin 22^\circ} = \frac{0.574}{0.375} = 1.53$ .
$\sin r = \frac{0.866}{1.33} = 0.651$ , so $r = 40.6^\circ \approx 41^\circ$ .
$v = \frac{3.00 \times 10^{8}}{1.52} = 1.97 \times 10^{8}\,\mathrm{m\,s^{-1}}$ .
$n = \frac{3.00 \times 10^{8}}{2.25 \times 10^{8}} = 1.33$ .
$\frac{0.80}{1.33} = 0.60\,\mathrm{m}$ .
$\sin \theta_a = 1.50 \times \sin 30^\circ = 0.750$ , so $\theta_a = 48.6^\circ$ .
The faces are parallel, so the ray meets the second face at the angle of refraction $r$ . Leaving the glass reverses the first refraction, so it emerges at the original angle $i$ : parallel, but displaced sideways. A ray along the normal is not bent at all and passes straight through, undisplaced.

Key points

Refraction is the change in direction of light crossing between media, because its speed changes. Angles are measured from the normal.
Snell's law: $n = \frac{\sin i}{\sin r}$ for light entering a medium from air; also $n = \frac{c}{v}$ .
Into a denser medium light bends towards the normal; out of it, away from the normal; along the normal, not at all.
A parallel-sided block shifts a ray sideways without changing its direction. Water looks shallower: $n = \frac{\text{real depth}}{\text{apparent depth}}$ .

Sources and credits

25.3: The Law of Refraction, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Consulted for the physics and the refractive indices; no text was copied.
Laser safety: Laser radiation: safety advice, UK Health Security Agency, updated 18 March 2025, Open Government Licence v3.0; summarised by Ganzaa.
Photo: Pencil in glass of water showing refraction (cropped).JPG by Meganbeckett27, Wikimedia Commons, licensed under CC BY-SA 3.0.
Video: Snell's Law (Refraction), A Level and GCSE Physics Revision, Kit Betts-Masters, embedded from YouTube.

Written by Ganzaa: the lesson text, both diagrams, the table of illustrative results, the worked examples and the practice exercises.

1The coin that comes back

2Experiment: tracing a ray through a glass block

3The laws of refraction

4Why light bends: a change of speed

5Light leaving a denser medium

6Through a parallel-sided block

7Real and apparent depth