Lesson Explainer: Refraction of Light Physics • 9th Grade

In this explainer, we will learn how to describe refraction as the speed and direction change of light when passing between media of different densities.

A cylindrical rod can be partially submerged in water. When the rod is viewed from above the surface of the water, the submerged part will appear to have turned through an angle. This is shown in the following figure.

However, the rod does not actually change shape. Rather, light from the submerged part of the rod changes direction, whereas the light from the rest of the rod does not.

The change of direction of the light as it passes from a medium to a different medium (such as from water to air) is called refraction.

The following figure shows the true shape of the rod and the change in the direction of two light rays due to refraction.

The following figure shows straight orange lines that have the same directions as the two light rays when they are in air. Following these orange lines back through the water, we see that the point at which the orange lines meet gives the apparent position of the end of the rod.

Let us look at an example identifying refraction of light.

Example 1: Identifying Refraction of a Light Ray

Which of the diagrams shows refraction of a light ray?

Answer

Refraction is the change of direction of the light as it passes from a medium to a different medium. The diagrams show light rays that are incident on different media to those that they initially travel in. The light ray cannot be seen inside the media.

In diagram A, the light ray does not enter the different medium, so it cannot be refracted.

In diagram C, the light ray does enter the different medium, but the ray does not change direction. The ray is not diffracted if it does not change direction.

In diagram D, the light ray presumably enters the new medium, as it does not reflect from it. The light ray does not exit the new medium, however, so it is impossible to say whether the ray is refracted. It is worth noting that the ray in diagram D is incident on the medium at the same angle as in diagram C in which no refraction occurred. We definitely cannot say that the light ray does refract in diagram D.

In diagram B, we can show the direction in which the light ray would travel if it did not change direction and hence the point at which the ray would emerge from the medium.

The light ray does not emerge from the point shown, so we can conclude that the light ray must have changed direction before it emerged. This light ray was refracted.

Refraction is a wave phenomenon. Refraction occurs because of differences in speeds at which waves travel in different substances.

The speed at which light waves travel in a medium is determined by a property called the absolute refractive index of the medium. This can just be called the refractive index. The refractive index is constant for a given substance. The refractive index has no unit.

Relationship: The Speed of Light in a Medium and the Refractive Index of the Medium

The absolute refractive index ๐‘› of a medium is related to the speed of light in the medium ๐‘ฃ and the speed of light in a vacuum ๐‘ by ๐‘›=๐‘๐‘ฃ, where ๐‘โ‰ˆ3ร—10/.๏Šฎms

The greater the absolute refractive index of a medium, the slower light waves travel in the medium.

A vacuum has a refractive index of exactly 1. All media other than a vacuum have refractive indices greater than 1. The refractive index of air is very close to 1 and can be approximated as exactly 1.

The refractive indices of different media are related to each other similarly to how the densities of these media are related to each other. Media of greater densities tend to have greater refractive indices than media of lower densities.

For light waves in a medium, the speed of the waves is ๐‘ฃ, where ๐‘ฃ=๐‘๐‘›โ‰ˆ3ร—10๐‘›/.๏Šฎms

The speed ๐‘ฃ of a wave is related to its frequency ๐‘“ and its wavelength ๐œ†. We can see this relationship using the formula ๐‘ฃ=๐‘“๐œ†.

This can be rearranged to make ๐‘“ the subject of the formula: ๐‘“=๐‘ฃ๐œ†.

We see then that for light waves, ๐‘“โ‰ˆ3ร—10๐‘›ร—1๐œ†โ‰ˆ3ร—10๐‘›๐œ†.๏Šฎ๏ŠฎHz

When light waves change the medium in which they travel, the frequency of the waves does not change.

We see then that for two light waves of the same frequency traveling in two media with different refractive indices ๐‘›๏Šง and ๐‘›๏Šจ, ๐‘“โ‰ˆ3ร—10๐‘›๐œ†โ‰ˆ3ร—10๐‘›๐œ†.๏Šฎ๏Šง๏Šง๏Šฎ๏Šจ๏ŠจHz

This means that the change in the speed of the waves is directly proportional to the change in the wavelength of the waves. The greater the refractive index of a medium, the shorter the wavelength of light is in the medium.

To better understand refraction, it is helpful at this point to consider the difference between a light ray and a light beam.

The difference between a light ray and a light beam is that a ray is a line, and it has zero thickness. A beam has nonzero thickness.

The following figure shows a model of a beam of light.

A light beam consists of light waves that have a wavelength ๐œ†. We can define wave fronts in the beam as imaginary lines that are one wavelength distant from each other. The length of a wave front is the thickness of a beam of light.

We can see that the beam has a direction of travel. As the beam travels, at each instant that it has traveled a distance ๐œ† in this direction, a new wave front is defined.

Let us now look at an example involving light waves moving in media of different densities.

Example 2: Comparing the Densities of Media That Light Waves Travel in

The diagram shows the wave fronts of four identical light waves traveling through water and then passing into four other materials.

  1. Which material is densest?
  2. Which material has a density most similar to the density of water?
  3. Which material has the lowest density?

Answer

The comparison between densities of materials can be taken as a comparison of the refractive indices of the materials.

The refractive indices of materials A, B, C, and D can be compared by comparing the wavelengths of light of a given frequency in them. The same frequency of light is incident on all the materials, as the question states that identical light waves pass from water into the material.

The distances between adjacent wave fronts for the beams of light shown traveling in the materials correspond to the wavelengths of light in that material for a given frequency of light. The greater the refractive index of the material, the shorter the wavelength of the light.

Part 1

The shortest distance between wave fronts is in material B. Material B is the densest.

Part 2

The material with the density closest to water is the material that has a distance between adjacent wave fronts most close to the distance for water. It is not immediately obvious if material A or material C best matches water. A diagram can help decide.

From the diagram, we see that the change in distance is greater from water to material A than from water to material C. Material C is then the closest in density to water.

Part 3

The material with the lowest density has the greatest distance between adjacent wave fronts. This is material D.

Refraction of a light beam occurs due to the unequal changes in the speed of different parts of the beam.

Let us consider a model of a beam of light passing from water into air.

We can see that between wave front 3 and wave front 4, the left-hand side of the beam has traveled in water, while the right-hand side of the beam has traveled in air. The right-hand side of the beam has therefore traveled farther than the left-hand side. The result of this difference in speed is that wave front 4 does not have the same direction as the preceding wave fronts. The beam therefore changes direction.

A beam moving perpendicularly to a boundary between two media generates wave fronts that are parallel to the boundary. When the beam reaches the boundary, all parts of the beam change speed equally. The first wave front generated in the new medium therefore has the same direction as the last wave front in the original medium. This means that a beam will not be refracted if it is incident on a boundary between media perpendicularly to the boundary.

The magnitude of a change of direction due to refraction that occurs during refraction depends on three quantities:

  • The refractive index of the medium the light passes from
  • The refractive index of the medium the light ray passes to
  • The angle of incidence of the light to the boundary between these two media

When determining the magnitude of a change of direction due to refraction, we can approximate a light beam with a light ray.

Let us again consider light passing from water to air, as shown in the following figure.

The dashed black line is the normal line to the boundary between water and air. We can see that the angle between the normal and the incident ray (the angle of incidence) is smaller than the angle between the normal and the emergent ray (the angle of refraction).

If a light ray instead passes from air to water, the angle of incidence will be larger than the angle of refraction.

In general, for a light ray passing between media, we see the following:

  • When the light ray passes into a medium of greater refractive index, it is deflected toward the normal line to the boundary between the media.
  • When the light ray passes into a medium of lesser refractive index, it is deflected away from the normal line to the boundary between the media.

The following figure shows a light ray refracted when it passes from a medium with refractive index ๐‘›i to a medium with refractive index ๐‘›f.

Mathematical manipulation that is outside the scope of the explainer can be used to state the relationship between ๐œƒi, ๐œƒr, ๐‘›i, and ๐‘›f in a formula. This formula is called Snellโ€™s law.

Formula: Snellโ€™s Law

For a light ray passing from a medium with refractive index ๐‘›i to a medium with refractive index ๐‘›f, the angle of incidence ๐œƒi is related to the angle of refraction ๐œƒr by ๐‘›๐œƒ=๐‘›๐œƒ.iifrsinsin

When a light ray moves from air to a denser medium, the value of ๐‘›i can be taken as approximately equal to 1. We can then write Snellโ€™s law as sinsin๐œƒ=๐‘›๐œƒifr or more simply as sinsin๐œƒ=๐‘›๐œƒ,ir where ๐‘› is the refractive index of the denser medium.

This formula can be rearranged as ๐‘›=๐œƒ๐œƒ.sinsinir

From this we can see that ๐œƒ=๏€ฝ๐‘›๐œƒ๐‘›๏‰riifsinsin๏Šฑ๏Šง and ๐œƒ=๏€ฝ๐‘›๐œƒ๐‘›๏‰.ifrisinsin๏Šฑ๏Šง

Let us now look at an example involving Snellโ€™s law.

Example 3: Calculating the Angle of Refraction of a Light Ray

A light ray traveling in air is incident on the flat surface of a plastic block with a refractive index of 1.5, hitting the surface at an angle of 45 degrees from the line normal to it. At what angle from the line normal to the surface does the refracted ray in the block travel? Answer to the nearest degree.

Answer

The light ray is initially in air. This allows us to use the simpler form of Snellโ€™s law ๐‘›=๐œƒ๐œƒ.sinsinir

The question asks us to calculate the angle between the line normal to the boundary between air and glass and the refracted ray. This is the angle of refraction ๐œƒr.

We therefore rearrange the formula to obtain sinsin๐œƒ=๐œƒ๐‘›.ri

Substituting the values given in the question, we have sinsin๐œƒ=451.5.rโˆ˜

The value of ๐œƒr is then given by ๐œƒ=๏€ฝ451.5๏‰.rsinsin๏Šฑ๏Šงโˆ˜

To the nearest degree, ๐œƒr is 28โˆ˜.

Let us now look at another example involving Snellโ€™s law.

Example 4: Calculating the Angle of Refraction of a Light Ray

A light ray traveling in water of refractive index 1.3 is incident on the flat surface of a plastic block with a refractive index of 1.6, traveling through the block at an angle of 45 degrees from the line normal to the surface. At what angle from the line normal to the surface does the incident ray strike the block? Answer to the nearest degree.

Answer

Both media in which the light ray travels have absolute refractive indices greater than 1. We must therefore use the full form of Snellโ€™s law ๐‘›๐œƒ=๐‘›๐œƒ.iifrsinsin

The question asks us to calculate the angle between the line normal to the boundary between air and glass and the incident ray. This is the angle of incidence ๐œƒi.

We therefore rearrange the formula to obtain sinsin๐œƒ=๐‘›๐œƒ๐‘›.ifri

Substituting the values given in the question, we have sinsin๐œƒ=1.6ร—451.3.iโˆ˜

The value of ๐œƒi is then given by ๐œƒ=๏€ฝ1.6ร—451.3๏‰.isinsin๏Šฑ๏Šงโˆ˜

To the nearest degree, ๐œƒr is 60โˆ˜.

We can consider light waves traveling from a medium A to a medium B that both have refractive indices greater than 1.

The relative refractive index ๐‘›relative for a light passing from a medium A to a medium B is related to the speed of light in medium A ๐‘ฃA and in medium B ๐‘ฃB by ๐‘›=๐‘ฃ๐‘ฃ.relativeAB

Let us now summarize what has been learned in this explainer.

Key Points

  • The change of direction of a light ray as it passes between media of different refractive indices is called refraction.
  • The absolute refractive index ๐‘› of a medium is related to the speed of light in the medium ๐‘ฃ and the speed of light in a vacuum ๐‘ by ๐‘›=๐‘๐‘ฃ, where ๐‘โ‰ˆ3ร—10/.vacuum๏Šฎms
  • A vacuum has an absolute refractive index of exactly 1.
  • Media of greater densities tend to have greater refractive indices.
  • The relative refractive index ๐‘›relative for a light passing from a medium A to a medium B is related to the speed of light in medium A ๐‘ฃA and in medium B ๐‘ฃB by ๐‘›=๐‘ฃ๐‘ฃ.relativeAB
  • When light waves change the medium in which they travel, the frequency of the waves does not change.
  • A light beam has wave fronts that are perpendicular to the direction of travel of the beam.
  • Refraction of a light beam occurs due to the unequal changes in the speeds of different parts of the beam.
  • A light beam will not be refracted if it is incident on a boundary between media perpendicularly to the boundary.
  • Snellโ€™s law states that for a light ray passing from a medium with absolute refractive index ๐‘›i to a medium with absolute refractive index ๐‘›f, the angle of incidence ๐œƒi is related to the angle of refraction ๐œƒr by ๐‘›๐œƒ=๐‘›๐œƒ.iifrsinsin
  • When a light ray moves between air and a denser medium, we can write Snellโ€™s law as ๐‘›=๐œƒ๐œƒ,sinsinir where ๐‘› is the refractive index of the denser medium.

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