If a wave meets a discontinuity where there is a change in speed in going from one medium to another, the energy carried by the wave will be reflected backed into the first medium and transferred into the second medium. The original wave is known as the incident wave. At the discontinuity a reflected wave and a transmitted wave (refracted wave) are formed.




Figure 1 shows a set of simulations for the propagation of surface water waves.


       Fig. 1a.   Propagation of a [2D] wave in a uniform medium with

                     no discontinuties.


       Fig 1b.    Propagation of a [2D] wave encountering a discontinuity

                    (normal incidentce). Only the incident and refracted

                     waves are shown.


       Fig 1c.    Propagation of a [2D] wave encountering a discontinuity

                    (oblique incidence). Only the incident and refracted

                     waves are shown. The refracted wave propagates in a

                     different direction to the incident wave.



A good example of reflection of sound is an echo. The fraction of energy carried by the echo can be almost as large as the energy of the incident wave if the surface is rigid and smooth.


       Fig. 2.   The reflection of a sound wave can produce an echo.


From smoth surfaces, waves are reflected such that the angle of incidence  is equal to the angle of reflection . 


(1)                           LAW OF REFLECTION for a smooth surface


The Law of Refraction applies to sound, light and all other forms of waves.



          Fig. 3.   Reflection from a smooth surface.



In a room with very reflective surfaces, sounds can become garbled. When sounds undergo multiple reflections, and persist after the sound has ceased emitting, we hear reverberations. If the surfaces are too absorbent, the sound level will be low and sounds will be dull and lifeless. In the design of concert halls, a balance must be achieved between reverberation and absorption. Highly reflective surfaces are often used to direct sound from the stage to the audience.


The Law of Reflection is also obeyed by particles reflected off straight smooth surfaces.




When any [2D] or [3D] wave traveling in one medium crosses a boundary into a medium where its velocity is different, the transmitted wave may move on in a different direction to the original the incident wave as shown in figure 1. This phenomenon is called refraction.


The refractive index  of a medium determines the propagation speed  of the wave. For a wave travelling from medium 1 into medium 2, then the ratio of the refractive indices is equal to the inverse of the velocity ratios




For electromagnetic radiation, the speed of light in a vacuum is always given by the symbol .  In a medium, where the speed of light  is less than , the speed  is determined by the refractive index  of the medium



                                                   light    = 2.9979x108  m.s-1


The direction of propagation of a wave is given by a straight arrow called a ray. The ray is drawn at right angles to the wavefront of the wave. The angles measured between the ray and the normal of the discontinuity define the angles of incidence, reflection and refraction.


Incident wave (medium 1)

       refractive index    speed      angle of incidence q1

Reflected wave (medium 1)

      refractive index     speed      angle of reflection

Refracted wave (medium2)

     refractive index     speed     angle of refraction


The direction in which the refracted ray travels is determined by Snell’s Law

        (4)                     Snell’s Law of Refraction 





and for the reflection

(1)                                      Law of Reflection



     Fig. 4.  Reflection and refraction at a discontinuity. When a wave

     travels into a medium of greater refractive index, the wave slows

     down and bends towards the normal. A wave that travels into a

     medium of smaller refractive index, speeds up and the wave will bend

     away from the normal. If the velocity increases, the refracted angle

     increases, and vice versa.


When a wave passes into a medium of lower refractive index, the light bends away from the normal. At a particular angle, the angle of refraction will be 90o and the refracted ray would skim the surface. The incident angle at which this occurs is called the critical angle . For angles of incident less than the critical angle, there will be refracted and reflected rays. For incident angles greater than the critical angle, there can be no refracted ray at all and the wave is reflected – this effect is called total internal reflection. N.B. total internal reflection only occurs where the medium beyond the discontinuity has a lower index of refraction. The total internal reflection is the principle behind fibre optics. Light can be transmitted along an optical fibre with almost zero energy loss. The light travels down the fibre only making glancing collisions with the walls so that total internal reflection occurs. Fibre-optic cabling is becoming more important in telecommunications (roll-out of the NBN) and in medicine (clear pictures of inside the body can be taken).

       Fig. 5.  total internal reflection with tiny fibres makes it possible

       to transmit light in complex paths with minimal loss.




Sound waves propagating through air are bent and undergo refraction when the air temperature varies (the higher the temperature, the greater the speed of sound). On a warm day, the air near the ground may be appreciably warmer than the rest of the air, so the speed of sound near the ground is greater. The sound will be refracted and bent away from the ground resulting in sound that does not seem to travel as far.  At night, the ground is cold and the speed of sound is less than the speed further above the ground, resulting in the sound being bent towards the ground. Sounds can be heard over considerably longer distances. N.B. refraction is caused by difference in the speed of propagation of waves (figure 6).


        Fig. 6.   Refraction of sound waves. Sound waves are bend in air

        of uneven temperatures.


We hear thunder when the lightning is close to us, but we often do not hear the thunder for distant lightning because of refraction – sounds travel slower at higher altitudes and bends away from the ground, so that we may not hear the thunder clap.


Refraction leads to a bending of the wavefronts when entering a new medium where the speed of the wave is different. To see why more clearly, we can consider a solder analogy as shown in figure 7. The solders are marching from firm ground (medium 1) into a muddy region (medium 2). The solders that reach the mud first are slowed down first and the row of solders bend. Look at figure 6 again – in warmer air, part of the wavefront moves faster than in colder air, so the bending of the wavefront is either away or towards the ground.

          Fig. 7.   Refraction: marching solders analogy.


The multiple reflections and refractions of ultrasonic waves are used by doctors for generating images inside our bodies. When high frequency (short wavelength) ultrasound enters the body, it reflects more strongly from the outside of an organ than from its interior, and an image of the organ is obtained.

        Fig. 8.   Image of a fetus using short wavelength ultrasonic waves.



Thinking Question:   PREDICT   OBSERVE   EXPLAIN

The refracted angle  is predicted using equation 4 (review figure 4)



Predict how the refraction angle   changes for variations in , , , , and  by making a series of scientific annotated diagrams.

Predict how the relative intensity of the reflected and refracted waves change as the parameters are changed. Think about a golf ball or a stone skipping across the surface of water.


        Maximum value of .


       List of refractive indices


Observe       Computer Simulation: Reflection and Refraction


Explain any discrepancies.





Examine the animations show in figure 1 carefully. From the animations, estimate (the dimensions of the square are 100 m x 100 m):

·        Period and frequency of the incident waves and refracted waves.

·        Wavelengths of incident waves and reflected waves.

·        The speed of the incident waves and reflected waves.

·        The relative refractive indices for the two media.

·        For oblique incidence, the angles of incidence and refraction. Check your answers using Snell’s Law.

Hint: use a sheet of thin paper to help make your measurements off the screen.





Doing Physics with Matlab

Download mscripts

Animation produced with     wm_refraction01.m    wm_refraction02.m



If you have any feedback, comments, suggestions or corrections please email:

Ian Cooper   School of Physics   University of Sydney