Lesson 5 of 10Light & Geometric Optics

Unit 4 · Lesson 5 of 10

Refraction, Index of Refraction and the Speed of Light

Why light bends when it crosses from one material into another, which way it bends, and how the index of refraction measures how much a material slows light down.

3 min read8 practice questionsInteractiveAsk AI about this →

Key things to remember

1Refraction is the change in direction of light at a boundary, caused by a change in speed.
2Index of refraction: $n = \frac{c}{v}$ , with $c = 3.00 \times 1 0^{8} m/s$ ; $n$ has no units and is at least 1.
3Into a larger $n$ (slower): bends toward the normal. Into a smaller $n$ (faster): bends away from the normal.
4A ray along the normal changes speed but not direction.
5Frequency stays the same across a boundary; speed and wavelength change.
6Common indices: air 1.00, water 1.33, crown glass 1.52, diamond 2.42.

Put a straw in a glass of water and it looks snapped at the surface. Look down into a pool and the bottom seems closer than it really is. Nothing is actually bent or moved: the light coming from the straw and the pool floor changes direction as it leaves the water. This bending of light at a boundary is called refraction, and it is the reason lenses, eyeglasses, cameras and your own eyes can focus light at all.

Refraction is caused by a change in speed

Light travels at

3.00 \times 1 0^{8} m/s

in a vacuum but more slowly in air, water, glass or diamond. When light crosses a boundary at an angle, the part of the beam that enters the new material first changes speed first, and the beam swings to a new direction.

Picture a shopping cart rolled at an angle off pavement onto grass. The front wheel that reaches the grass first slows down while the other front wheel is still rolling quickly on pavement, so the cart turns toward the grass side. Light behaves the same way. A ray that meets the boundary head-on (along the normal, at $0^{\circ}$ ) changes speed but does not change direction, because both 'wheels' reach the new material at the same moment.

Fig 1Two panels. Light passing from air into water slows down and bends toward the normal (45° in air becomes about 32° in water). Light passing from water into air (30° becomes about 42°) speeds up and bends away from the normal. A fainter partially reflected ray appears in each panel.

Angle of refraction $∠ R$ : the angle between the refracted ray and the normal (measured from the normal, as always).
Into a slower medium (larger $n$ ): the ray bends toward the normal, so $∠ R < ∠ i$ .
Into a faster medium (smaller $n$ ): the ray bends away from the normal, so $∠ R > ∠ i$ .
Along the normal ( $∠ i = 0^{\circ}$ ): no bending at all.
Some light is usually reflected at the boundary too (partial reflection), which is why you can see a faint reflection in a window.

Index of refraction

n = \frac{c}{v}

Index of refraction n equals the speed of light in a vacuum c divided by the speed of light in the medium v. It has no units.

Medium	Index of refraction $n$	Speed of light ( $\times 1 0^{8} m/s$ )
Vacuum	1 (exactly)	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
Acrylic (Plexiglas)	1.49	2.01
Crown glass	1.52	1.97
Diamond	2.42	1.24

Indices for yellow light. Ordinary glasses range from about 1.50 to 1.52; problems in this unit state which value to use.

Light in any ordinary transparent material is slower than $c$ , so its $n$ is greater than 1. A bigger index means slower light and more bending. Diamond's very large index of 2.42 means light inside it travels at less than half its vacuum speed, which is part of why diamonds sparkle so much.

Optical density is not mass density

A material with a higher index of refraction is called 'optically denser', but that has nothing to do with mass per volume. Rubbing alcohol (isopropyl alcohol) is less dense than water (about 0.79 g/mL versus 1.00 g/mL), yet its index (about 1.38) is higher than water's 1.33.

What changes and what does not

When light enters a new medium its speed changes and its wavelength changes by the same factor, but its frequency stays the same, because the frequency is set by the source. Red light is still red underwater. Light of wavelength 600 nm in air has a wavelength of about

600 \div 1.33 = 451 nm

in water.

The index of refraction is slightly different for each colour: violet light slows down a little more than red light in glass, so it bends a little more. A prism uses this to spread white light into a rainbow of colours, an effect called dispersion. It is also part of how real rainbows form, as you will see in the lesson on total internal reflection.

Loading interactive…

Pick two media and an angle of incidence to see the ray bend toward or away from the normal, with the speed of light in each medium shown.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1

Find the speed of light in water (

n = 1.33

Example 2

Light travels through an unknown transparent solid at

1.97 \times 1 0^{8} m/s

. Find its index of refraction and identify it from the table.

Example 3

A ray of light passes from water into air, striking the surface at an angle of incidence of

3 0^{\circ}

. Without calculating, decide whether the angle of refraction is larger or smaller than

3 0^{\circ}

, and explain.

Where marks get lost

Saying light bends away from the normal when it slows down. Slower medium (larger $n$ ) means bending toward the normal.
Writing $n = \frac{v}{c}$ upside down. Since $v$ is never more than $c$ , an index below 1 is a sign the fraction was flipped.
Giving the index of refraction units. It is a ratio of two speeds, so the units cancel.
Assuming a ray along the normal bends. At $0^{\circ}$ incidence the speed changes but the direction does not.
Thinking frequency (colour) changes when light enters water. Speed and wavelength change; frequency stays the same.

Flashcards 8

Refraction

Index of refraction

Light entering a medium with larger n

Light entering a medium with smaller n

+ 4 more

Practice

Find the speed of light in diamond (

n = 2.42

) in units of

1 0^{8} m/s

, to 2 decimal places.

× 10⁸ m/s

Light travels through glycerin at

2.04 \times 1 0^{8} m/s

. What is the index of refraction of glycerin, to 2 decimal places?

A ray of light passes at an angle from air into glass. What happens?

Which property of light stays the same when it passes from air into water?

Sort these media from the one in which light travels fastest to the one in which it travels slowest.

1Water ( $n = 1.33$ )
2Diamond ( $n = 2.42$ )
3Crown glass ( $n = 1.52$ )
4Air ( $n = 1.00$ )

What is the name of the quantity found by dividing the speed of light in a vacuum by the speed of light in a medium?

How many times faster does light travel in water (

n = 1.33

) than in crown glass (

n = 1.52

)? Give 2 decimal places.

A laser beam strikes the flat surface of a block of glass exactly along the normal. What happens to the beam as it enters the glass?

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