Refraction of waves



When waves move from one medium to another, the speed of the wave changes, this causes wave to bent and the bending of wave is called Refraction of wave. The diagram below illustrate why refraction occur.

Refraction of light wave

When light wave travel between two medium of different optical density, the speed of the light changes. This causes a change in the direction of the propagation of light, therefore Refraction takes place.

Angle form between the Incident ray and the Normal is called angle of incidence, i.

Angle form between the Refracted ray and the Normal is called angle of refraction, r.

A medium in which the velocity of light is lower is an optically denser medium.

When light travels from an optically less medium to an optically denser medium, it bends towards the Normal, vice versa when light travels from a less dense medium to a more dense medium, it bends away from Normal.


Snell's Law

i = angle of incident in the less dense medium

r = angle of refraction in the more dense medium

n = refractive index

Refraction can only occur light travels to a medium of different density and the angle of incident is not equal to 0.

When a ray of light crosses the boundary between two different mediums at right angle,

  1. angle of incident, i = 0
  2. light does not bend, no refraction take place,
  3. the speed of light still changes accordingly.




Phenomena of refraction of light in our daily lives

A river appear to be shallower than it actually is.









Refraction of light wave causes a pencil in the water to look bent

The fish we see swimming in the water is only its image. The fish is actually in a deeper position.

A fish or a diver under water can see everything above the surface. However, their scope of view is squeezed into a cone of angle 98 degree (twice the critical angle of water).

Flattering of the Sun


Rays from top of sun are also refracted, but not as much because they enter the atmosphere at a less oblique angle. Thus, the top of the sun is also flattened, but not as much as the bottom.




Critical Angle

When rays of light pass from a denser medium to a less dense medium, e.g. from water to air, the rays are refracted away from the normal. The angle of refraction is larger than the angle of incidence. According to Snell's law, the greater the angle of incidence, i, the greater is the angle of refraction, r. However, there is a limit. For a certain angle of incidence, i, when the angle of refraction, r is 90 degree, the refracted ray moves along the boundary between water and air. The angle of incidence, i in the denser medium at this limit is called the critical angle, c.

Critical angle, c is defined as the angle of incidence in the denser medium when the angle of refraction, r in the less dense medium is 90 degree.

If the angle of incidence, i is increased further so that it is greater than the critical angle, c (i > c), the light is no longer refracted but is internally reflected. This is called Total Internal Reflection. Look at the animation and the diagram on the right.


The above picture shows a green laser incident to a piece of right angle 45 degree prism. The ray encounters 4 total internal reflections before emerging out.

Total Internal Reflection

Total Internal Reflection will only occur when:

  1. light travel from a more dense medium to a less dense medium and

  2. the angle of incidence, i, is greater than the critical angle, c. (i>c)

In our daily living, there are a lot phenomena that take place because of Total Internal Reflection.

Natural Phenomena involving Total Internal Reflection

The surface of the water acts as a mirror, because of Total Internal Reflection.

A diver is able to see a fish swimming in the air! Click here to find out how.

Fish's eye view

Rays A and B are totally internally reflected. Therefore the fish can see the worm. Outside the 98 degree cone, the fish sees light reflected from the pond.


On a hot day we may often see what appears to be a puddleof water on the road ahead of us only to have it disappear when we get there. Look at the picture on the right.

This is because the air above the ground is hotter (less dense) than the air higher up. Light from the sky and the cloud is refracted gradually towards the horizontal after passing through the different layers of air of decreasing densities. The incident angle becomes greater and greater. Eventually the light ray meets a layer of air near the ground at an angle greater than the critical angle so total internal reflection takes place and the light is reflected upwards towards our eyes. We see the image of the sky and the clouds on the surface of the road as a puddle of water.

Sunrise and Sunset

The Sun that we see during sunrise and sunset is only an image.

Light entering the atmosphere is refracted by layers of air of different densities producing an apparent shift in the position of the sun. The sun is visible at the horizon about 2 minutes before the actual sunrise, and about 2 minutes after the actual sunset.


The rainbow's appearance is caused by dispersion of sunlight as it is refracted by (approximately spherical) raindrops. The light is first refracted as it enters the surface of the raindrop, undergoes total internal reflection from the back of the drop, and is again refracted as it leaves the drop. The overall effect is that the incoming light is reflected back at an angle of about 40-42o, regardless of the size of the drop. Since the water of the raindrops is dispersive, the amount that the sunlight is bent depends upon the wavelength (colour) of the light's constituent parts. Blue light has a shorter wavelength than red light. Blue light is refracted at a greater angle than red light, but because of the reflection from the back of the raindrop, the red light appears higher in the sky, and forms the outer colour of the rainbow.

Sometimes, a second, dimmer rainbow is seen outside the primary rainbow, caused by a double total internal reflection of the sunlight inside the raindrops, and appears at an angle of 50-53o. Because of the extra reflection, the colours of the bow are inverted compared to the primary bow, with blue on the outside and red on the inside. From an aeroplane one has the opportunity to see the whole circle of the rainbow, with the plane's shadow in the centre.




Circular rainbow. View from a hot air balloon

Experiment of Total Internal Reflection

Experiment 1

What to Do

  1. Make a small round (~5mm) hole in the side of the bottle near the base..

  2. Put your finger over the hole and fill the bottle up with water.

  3. Shine the torch through the bottle at the back of the hole

  4. Remove your finger from the hole and move it down the stream of water.

What may Happen

You should notice a spot of light on your hand while it is in the stream of water. It tends to work best when the water comes out quite slowly.

Experiment 2

The spoon is at the bottom of the bowl. But looking from the bottom of the bowl, the spoon looks floating on the surface of the water. The water surface looks like a silvered mirror.

Application of Total Internal Reflection



The prism inside the reflector reflects the incident light by total internal reflection.


The critical angle for diamond in air is only 24.5 degrees. Diamonds are cut at chosen angles so that most rays, incident on them exceed the critical angle. Any ray which strikes the surface on the inside at an angle of greater than 24.5 degrees will not escape the diamond but is reflected back into the diamond and eventually exiting from the top surface to give the diamond its sparkle.

Binocular & Periscope





Magnifying power of binoculars is made larger by increasing the path length traveled between the two lenses.

Optical Fibre

An Optical Fibre is a very thin, flexible rods made of special glass or transparent plastic (diameter of about 0.01mm). The fibre has a high refractive index. Therefore its critical angle is small. Light enters with an angle of incidence which is greater than the critical angle of the glass. Total internal reflections take place repeatedly until it emerges at the other end of the fibre.

  • The inner core is made of optically more dense glass.
  • The outer cladding is made optically less dense glass.

In Telecommunication, copper cables are now replaced by fibre optics cables in the telephone system. Multiple signals can be sent at high speeds through bundles of fibres by using flashes of light from a laser.

The advantages of using optical fibre over electrical wires in telecommunication:

  1. much more information can be transmitted because almost he entire light energy (which carries information) experiences total internal reflection in the optical fibre.
  2. free from electromagnetic field interference resulting in clearer connection.
  3. free of electrical resistance.
  4. no hazard of electrocution if cable breaks.
  5. cheap, light and easily handled.
View this video about optical fibre..

In Medicine. Light entering one end of an optical fibre experiences multiple Total Internal Reflections as it propagates through the whole length of the fibre before emerging at the other end. Optical fibres are used to examined the internal organs of patients, such as the colon and stomach, without operating on the patient. This method is called Endoscopes.

Refraction of water waves

When water waves move from water of different depth, the speed of the water waves change. This cause the direction of the water wave to change. Water wave travel faster in deep water than in shallow water. Hence refraction (bending) of water wave occurs. The decrease in speed will also be accompanied by a decrease in wavelength.

Characteristics of Refraction of waves:
  1. The frequency remains the same after refraction.
  2. The wavelength, speed and direction of the propagation of the wave change after refraction.
  3. λdeep > λshallow
  4. vdeep > vshallow

Video clips on refraction of water wave and here too.When water wave moves from deep water into shallow water, the wave is refracted towards the normal. Conversely, the wave is refracted away from the normal when it is transmitted from shallow water into deep water. Water waves travel faster in deep water than in shallow water. The wavelength of water wave is longer in the deep water.

Refraction of water waves seen from a ripple tank. A piece of glass immersed in the water creates a shallow region in the ripple tank.

Phenomenon of the refraction of water wave

  1. Why is sea water in the deep end look stationary compared to water by the shore?
  2. Why does sea water waves follow the shape of the beach?

This is because the wavelength of water waves at the deep end is longer than at the shallow end. Wavefronts are parallel to one another at the deep end. As water waves approach a cape, they enter into a region of shallow water. The speed and wavelength reduces compare to that of at the bay. Water waves are refracted and take the shape of the beach. Look at the pictures below.

  • Occurs when waves move into shallow water and "feel" the bottom



  1. Why is the sea turbulent at the cape but calm at the bay?

As water wave propagate from deep region to the shallow region near the shore, part of wave in shallow water slows down, part of wave in deeper water moves more quickly. As a result refraction of wave takes place and wave bends. Wave energy is converged towards the cape (headland) but diverged away from the bay. Wave energy dissipated in bays. Therefore sea is rough at the cape but calm at the bay.

Refraction of sound wave

Sound waves is refracted  when they travel in mediums of different density. Sound travels slower in a more dense medium than in a less dense medium. Sound waves are refracted towards the normal when they travel from a less dense medium to a more dense medium. Vice visa they are refracted away from the normal when they move from a more dense medium to a less medium.

Phenomenon of the refraction of sound waves

Sound propagates in all directions from a point source. Normally, only that which is initially directed toward the listener can be heard, but refraction can bend sound downward. Normally, only the direct sound is received. But refraction can add some additional sound, effectively amplifying the sound. Natural amplifiers can occur over cool lakes.

Sound of a moving train at a distance is clearer at night than in the day time. This is due to the effects of refraction of sound waves. Sound waves undergo refraction when they pass through layers of air which are at different temperature (different density). At night the layers of air close to the ground are cooler than the layers further from the ground. Sound wave travels at a slower speed in cold air (more dense). As a result the sound waves are refracted away from normal. This refraction is repeated until the angle of incidence is more than the critical angle and therefore total internal reflection takes place. As a result sound wave is refracted in the path of a curve  towards the ground instead of disappearing into the upper layers of the air.


Refraction of sound wave during day time. Air above the ground is hotter (< dense) than the air (colder and > dense) higher up. Therefore sound wave is refracted away from the normal and disappearing into the upper layers of the air.

Click here to view Refraction of sound waves.

Click here to view experiment on refraction of sound waves.

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