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Refraction of Light

by Ron Kurtus (revised 15 October 2012)

When visible light passes through a transparent material such as glass, its velocity changes according to the Index of Refraction of the material. This slowing is caused by the electrical fields in the material.

When the beam of light enters the material at an angle, it is bent or refracted as a result of the decrease in velocity. The refraction is similar to the change in direction of soldiers marching into a muddy field.

Questions you may have include:

This lesson will answer those questions. Useful tool: Units Conversion



Light slows down in a material

Visible light is electromagnetic radiation or waveform. The speed of light in a vacuum is about 186,000 miles per second or 300,000 kilometers per second.

(Note: Velocity is speed in a specific direction. If we don't care in what the direction the light is traveling, we usually call it speed of light. However, if the light is specifically traveling in some direction through a material, velocity of light is the correct term.)

The velocity of light or other electromagnetic radiation is typically slower when it passes through a transparent material. For example, the speed of light in water is about 140,000 mi/sec or 226,000 km/sec.

Electrical fields slow it down

The reason electromagnetic radiation is slower when the light passes through a transparent material such as water or glass is because of the effect of the electrical fields surrounding the electrons and nuclei of the atoms in the material.

The fields almost act like a "friction" on the light wave, thus slowing it down. It is like trying to walk through a muddy field.

Velocity different for each wavelength

The speed of light in a transparent material is slightly different for each wavelength. That characteristic is called dispersion and responsible for the creation of the spectrum in a prism.

(See Dispersion of Light for more information.)

Index of refraction

The measurement of how much the speed is slowed is indicated by the Index of Refraction of the material.

The Index of Refection (i) of a material equals the speed of light in a vacuum (c) divided by the speed of light in the material (cm). Since c and cm are in meters/second or miles/second, i is simply a number or ratio.

i = c/cm

Or, if you want to find cm:

cm = c/i

Since cm varies slightly with wavelength, the value for green light is used as a good average number.

Different materials

The following chart shows the index of refraction for several materials:

Material

Index of Refraction

air

1.0002926

water

1.333

glass

(typical) 1.5 to 1.9

diamond

2.419

Usually, the index of refraction for air is just considered as 1.00, since the amount greater is too small to make a difference in most calculations.

Speed in glass

For example, the speed of light through a piece of glass with an index of refraction of i = 1.5 is:

cm = 186,000/1.5 = 124,000 miles/sec.

or

cm = 300,000/1.5 = 200,000 km/sec.

Bending light

When a beam of light passes at an angle from one material to another, the beam is bent or refracted according to the difference in speed in the second material compared with the first. Calculation of the refraction angle is determined according to Snell's Law.

(See Snell's Law for the Refraction of Light for more information.)

Reason beam bends

Considering a group of soldiers marching into a muddy field at an angle to their direction of travel can explain how a beam of light will be refracted. As the soldiers try to stay in a line, the direction of travel would bend because marching in mud would slow them down, starting with the first group to enter the field. Then, as they leave the muddy area, they go to their original speed, thus bending the direction of travel again. The original direction and the final direction are parallel but displaced.

The same thing happens when a beam of light enters a transparent material at an angle.

Light moving from air to glass and back to air

Light moving from air to glass and back to air

Does color change in material?

You might wonder if the color of the light changes when moving into another material. In the picture above, it shows that the wavelength seems shorter in the material where the light travels slower. Actually, your eyes perceive color by the frequency (waves per second) and not wavelength.

The relationship between the speed of light, frequency and wavelength is:

c = νλ

where ν is the frequency (Greek letter nu) and λ is the wavelength (Greek letter lambda).

(Note: some browsers may not display the Greek letters properly).

Now the speed of light in the material is:

cm = νλm

where λm is the wavelength in the material

But the frequency ν remains the same and thus the perception of color is the same. You can verify this by looking at objects when you are swimming under water. The speed is slower under water, but the color remains the same.

Pencil in water glass

You can see this effect by putting a pencil in a glass of water. It appears as if the pencil is broken, but it is just because of the refraction of light.

Pencil in water glass

Pencil in water glass

The light from the pencil is refracted as it passes from the water to the glass to air, causing it to be displaced. Since the surface of the glass is curved, the water in the glass also acts as a magnifying glass, slightly enlarging the pencil.

Relationship to wavelength

The speed of light in a material is also a function of the wavelength or frequency of the light. That means that the Index of Refraction is different for different wavelengths. In glass, the speed of light—and thus the Index of Refraction—changes by about 2% between primary colors of visible light (red, yellow, orange, green, blue, indigo, violet).

To avoid confusion, the Index of Refraction is usually stated as an average or for the color green. The effect of the different speeds shows up in the effect called dispersion, where the light is refracted at different angles for each color.

(See Dispersion of Light for more information.)

Summary

When visible light passes through a transparent material such as glass, its velocity changes according to the index of refraction of the material. The index of refraction of air is about 1.00 and that of water is 1.33. When the beam of light enters the material at an angle, it is bent or refracted as a result of the decrease in velocity. The property of refraction is important in the making of lenses.


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Resources and references

Ron Kurtus' Credentials

Websites

Refraction of Light - From the University of Missouri

Physics Resources

Books

Schaum's Outline of Optics by Eugene Hecht; McGraw-Hill (1974) $16.95

Introduction to Modern Optics by Grant R. Fowles; Dover Publications (1989) $16.95

Optics by Eugene Hecht; Addison Wesley (2001) $108.00 - Textbook covers wave motion, electromagnetic theory, propagation of light, geometrical optics, superimposition of waves, polarization, interference, diffraction, fourier optics and lasers


Questions and comments

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