E. Physics: Light and Geometric Optics · Light and Geometric OpticsRefraction and the Index of Refraction
E2.6 E3.7 E2.1 A1.12 A1.13About 70 minutes
Learning goals- I can explain refraction as a result of light changing speed.
- I can calculate the index of refraction (n = c/v) and the speed of light in a medium.
- I can predict whether light bends towards or away from the normal.
- I can describe the factors that affect how much light refracts.
Words to know
refraction
The change in direction of light as it passes at an angle from one medium into another.
medium
The material light travels through, such as air, water or glass.
index of refraction (n)
The ratio of the speed of light in a vacuum to its speed in a medium: n = c/v.
angle of refraction (θR)
The angle between the refracted ray and the normal.
refracted ray
The ray that travels into the second medium after refraction.
optically denser
Having a larger index of refraction (light travels more slowly).
wavefront
A line joining the crests of a wave; it is perpendicular to the ray.
dispersion
The separation of white light into colours because different colours refract by different amounts.
The broken pencil
Put a pencil in a glass of water and look from the side. The pencil seems to bend or even break at the water's surface. The pencil hasn't changed. The light coming from it has: it changed direction as it left the water. This bending of light is called refraction.
Refraction is the change in direction of light as it passes at an angle from one medium (material) into another. It happens because light travels at different speeds in different media.
Remember from Grade 4
In Grade 4 you learned that light bends when it passes from air into water or glass, and that lenses and prisms use this bending. Now you will measure it, explain it with the speed of light, and calculate it.
The speed of light depends on the medium
Light travels at c = 3.00 × 10⁸ m/s in a vacuum. In any material it is slower, because it interacts with the particles of the material. Air slows it only a tiny bit; water slows it by about 25%; diamond slows it to less than half.
We compare speeds with the index of refraction (n):
n = c / v
where c is the speed of light in a vacuum and v is the speed of light in the medium. Because it is a ratio of two speeds, n has no units. It is always 1 or more. The larger n is, the slower light travels in that medium. A medium with a larger n is often called optically denser.
| Medium | Index of refraction (n) | Speed of light (× 10⁸ m/s) |
|---|
| vacuum | 1.00 (exactly 1) | 3.00 |
| air | 1.0003 (use 1.00) | 3.00 |
| ice | 1.31 | 2.29 |
| water | 1.33 | 2.26 |
| ethanol | 1.36 | 2.21 |
| glycerol | 1.47 | 2.04 |
| acrylic (Plexiglas) | 1.49 | 2.01 |
| crown glass | 1.52 | 1.97 |
| zircon | 1.92 | 1.56 |
| diamond | 2.42 | 1.24 |
Worked exampleExample 1: Speed of light in water
The index of refraction of water is 1.33. What is the speed of light in water?
- Given: n = 1.33, c = 3.00 × 10⁸ m/s. Required: v.
- Rearrange n = c / v to get v = c / n.
- v = (3.00 × 10⁸ m/s) ÷ 1.33 = 2.26 × 10⁸ m/s.
v = 2.26 × 10⁸ m/s: about 75% of its speed in a vacuum.
Worked exampleExample 2: Identify a mystery liquid
Light travels through a clear liquid at 2.04 × 10⁸ m/s. Find the index of refraction and use the table to identify the liquid.
- n = c / v = (3.00 × 10⁸) ÷ (2.04 × 10⁸)
- n = 1.47
- In the table, n = 1.47 matches glycerol.
n = 1.47: the liquid is probably glycerol.
Which way does light bend?
The angle of refraction (θR) is the angle between the refracted ray and the normal. Two rules describe the direction of bending:
- When light passes into a medium where it travels more slowly (larger n), it bends towards the normal: θR < θi.
- When light passes into a medium where it travels faster (smaller n), it bends away from the normal: θR > θi.
- If light hits the boundary along the normal (θi = 0°), it slows down or speeds up but does not bend.
At the same time, a little of the light is reflected at the boundary. This partial reflection is why you can see a faint reflection in a shop window. (More about this in the total internal reflection lesson.)
Why does slowing down cause bending?
Picture a marching band crossing at an angle from a paved parking lot onto a muddy field. The marchers on one end of each row reach the mud first and slow down, while the rest of the row is still marching quickly on pavement. The row swings around and the band heads off in a new direction, more directly across the boundary.
Light waves do the same thing. Draw lines joining the crests of a light wave (wavefronts). When a wavefront meets a slower medium at an angle, one end slows first, so the wavefront turns. The frequency of the light does not change (the source sets it), so by v = f λ, the slower light has a shorter wavelength: λ in the medium = λ in a vacuum ÷ n.
Worked exampleExample 3: Wavelength inside water
Red light from a laser pointer has a wavelength of 650 nm in air. What is its wavelength in water (n = 1.33)? Does its colour change?
- The frequency stays the same, and v = f λ, so λ is proportional to v.
- λ_water = λ_air ÷ n = 650 nm ÷ 1.33 = 489 nm.
λ ≈ 489 nm in water. The light still looks red to a diver: the colour we see depends on the light's frequency, which does not change.
What affects how much light refracts?
- The two media. The bigger the difference in index of refraction (speed), the more the light bends. Air to diamond bends light much more than air to water.
- The angle of incidence. At 0° there is no bending. The larger the angle of incidence, the larger the change in direction.
- The colour (wavelength) of the light. In glass and water, violet light travels slightly more slowly than red light, so n is slightly larger for violet and violet bends a little more. This is called dispersion, and it is why prisms and raindrops split white light into colours.
- Temperature and density of air. Warm air is less dense than cold air and has a slightly smaller index of refraction. Layers of different air bend light gradually, causing mirages and shimmering (see the natural phenomena lesson).
Just for funLight is so fast that even after water "slows it down", it still travels about 226 000 km every second. Slow is relative.
Hands-on activityBending light at home
You need: a clear glass or straight-sided plastic container, water, a pencil, a flashlight, a comb or a card with a narrow slit, a few drops of milk, a dark room.
- The broken pencil. Put the pencil in a glass of water at an angle. Look from the side and from above. Sketch what you see.
- See the beam. Fill a straight-sided container with water and stir in 2 or 3 drops of milk (the tiny milk particles scatter light so the beam becomes visible). In a dark room, shine a thin beam (flashlight through a comb gap) down into the water at an angle through the surface.
- Sketch the beam above and below the surface. Draw the normal. Did the beam bend towards or away from the normal as it entered the water?
- Shine the beam straight down (along the normal). Does it bend?
- Write a conclusion that uses the words speed, normal and index of refraction.
What to look for: the beam bends towards the normal as it enters the water and does not bend when it travels along the normal. The pencil looks broken and the underwater part looks raised.
Safety (grown-up note): Wipe up spills so no one slips. Keep the flashlight dry.
Your turn
1Define refraction and explain what causes it.
Refraction is the change in direction of light as it passes at an angle from one medium into another. It is caused by the change in the speed of light.
2Write the equation for the index of refraction and state what each symbol means.
n = c / v: n = index of refraction, c = speed of light in a vacuum (3.00 × 10⁸ m/s), v = speed of light in the medium.
3Calculate the speed of light in diamond (n = 2.42).
v = c / n = (3.00 × 10⁸) ÷ 2.42 = 1.24 × 10⁸ m/s.
4Light passes from water into air at an angle. Does it bend towards or away from the normal? Why?
Away from the normal, because it speeds up (air has a smaller n).
5Light enters a glass block along the normal. What happens?
It slows down but does not bend.
6Why can n never be less than 1 for an ordinary material?
n = c / v, and light in a material is never faster than c, so v ≤ c and n ≥ 1.
More practice: warm-up
1What is the index of refraction of a vacuum?
2Which is optically denser, water (n = 1.33) or glass (n = 1.52)?
Glass (larger n, slower light).
3What is the angle of refraction measured from?
4Does the frequency of light change when it enters water?
No. Only its speed and wavelength change.
5Name the bending of different colours by different amounts.
More practice: on your own
1Light travels at 1.97 × 10⁸ m/s in a type of glass. Find n.
n = (3.00 × 10⁸) ÷ (1.97 × 10⁸) = 1.52 (crown glass).
2How long does light take to travel through a 2.0 cm thick glass window (n = 1.52)? Compare with the time through 2.0 cm of air.
v = 1.97 × 10⁸ m/s. t = 0.020 m ÷ 1.97 × 10⁸ m/s = 1.0 × 10⁻¹⁰ s. In air: t = 0.020 ÷ 3.00 × 10⁸ = 6.7 × 10⁻¹¹ s. Glass takes about 1.5 times as long.
3Rank these media by the speed of light, fastest first: diamond, air, water, acrylic.
Air (1.00), water (1.33), acrylic (1.49), diamond (2.42): smaller n means faster light.
4Explain the marching-band model of refraction.
When a row of marchers crosses a boundary at an angle, the marchers who reach the slower ground first slow down while the others keep their speed, so the row turns. A light wavefront turns the same way when part of it enters a slower medium first.
5Green light has λ = 530 nm in air. Find its wavelength in glass (n = 1.52).
λ = 530 nm ÷ 1.52 = 349 nm (it is still the same frequency, so still the same colour).
Challenge
1Light enters a block of an unknown material and its wavelength drops from 600 nm to 413 nm. Find n and the speed of light in the block. What might the material be?
n = 600 ÷ 413 = 1.45 (speed drops by the same factor). v = 3.00 × 10⁸ ÷ 1.45 = 2.07 × 10⁸ m/s. This is close to fused quartz (n ≈ 1.46), a kind of glass; it is not exactly any material in the table.
2A ray passes from air into a layer of water with parallel top and bottom surfaces, then out through the bottom into air again (ignore the container). Is the final ray parallel to the incident ray? Explain.
Yes. Entering the water it bends towards the normal by a certain amount; leaving through a parallel surface, it bends away from the normal by exactly the reverse amount, so it leaves parallel to its original direction, just shifted sideways.
3Explain why a prism splits white light into colours but a flat glass window does not seem to.
In both, violet bends slightly more than red (dispersion). In a window the two surfaces are parallel, so the second refraction undoes the first and the colours leave parallel and overlapping. In a prism the surfaces are angled, so the second refraction adds to the spreading and the colours separate.
Quiz
1. The index of refraction is calculated with:
2. Light passes from air into glass at an angle. It:
3. The speed of light in water (n = 1.33) is about:
4. Light strikes a boundary along the normal. It:
5. When light enters a medium with a larger index of refraction, which quantity stays the same?
6. In which medium does light travel slowest?
Big idea: Light changes speed in different media; that change in speed causes refraction (E2.6, E3.7). The index of refraction n = c/v measures how much a medium slows light. Bending towards the normal means slowing down; away means speeding up.
Common difficulties:
- Towards vs away. Link it to speed: slow → towards the normal ("slow down and turn in").
- Measuring from the surface. Angles are measured from the normal, just as in reflection.
- Thinking colour changes underwater. Colour depends on frequency, which stays the same.
How to help: The milk-in-water beam activity is quick and striking. Ask your teen to explain the broken-pencil effect at the dinner table using the word "speed".