1) Applet > Java Simulation
(Please remember to allow running of scripts/ActiveX controls for viewing the applet)
2) Theory
- Snell's Law
Figure 1 Reflection and refraction with longitudinal and
transverse waves
From Figure 1, it can be seen that when
there is a longitudinal or transverse incident wave at the interface between two
mediums, there can be a maximum occurrence of two reflected waves and two
refracted waves. The angle of reflection and refraction can both be calculated
from Snell's law.
Table 1 List of Symbols for Snell's law
| Symbol | Meaning |
 | angle of incidence |
 | angle of reflection for longitudinal wave |
 | angle of reflection for transverse wave |
 | angle of refraction |
 | angle of refraction for longitudinal wave |
 | angle of refraction for transverse wave |
 | sound velocity in medium 1 |
 | sound velocity of longitudinal wave in medium 1 |
 | sound velocity of transverse wave in medium 1 |
 | sound velocity in medium 2 |
 | sound velocity of longitudinal wave in medium 2 |
 | sound velocity of transverse wave in medium 2 |
The general form of Snell's law
is:
Snell's law can be used to calculate the
angles of reflection and refraction when the incident wave is a longitudinal or
transverse wave.
When the incident wave is a
longitudinal wave,
| Angle of Interest | Equivalent form of Snell's law to be used |
|  |
|  |
|  |
|  |
When the incident wave is a transverse
wave,
| Angle of Interest | Equivalent form of Snell's law to be used |
|  |
|  |
|  |
|  |
You may wish to practise the Snell's law
using the values given in Table 2. The result can be verified by our link at> Java Simulation of Snell's Law.
Table 2 Ultrasonic Wave Velocities (mean values
in km/s)
| Materials | Longitudinal Wave Velocity(km/s) | Transverse Wave Velocity (km/s) |
| Aluminum | 6.300 | 3.080 |
| Steel | 5.900 | 3.230 |
| Perspex | 2.700 | 1.300 |
| Water | 1.490 | - |
| Air | 0.344 | - |
- Critical Angles & Surface Wave
When the angle of refraction, β, equals
to 90o, the angle of incidence, α, is referred as the critical
angle. At the interface between 2
mediums, there is a maximum possibility of 2 critical angles.
The 1st
critical angle occurs when the refracted longitudinal wave disappears as shown
in figure 2.
The 2nd critical angle occurs when the refracted transverse
wave disappears as shown in figure 3.
At
the 2nd critical angle, a surface wave (Rayleigh wave) is created and total
reflection starts from there.
Figure 2 1st critical angle when the refracted
longitudinal wave disappears
Figure 3 Surface Wave formed
at the 2nd critical angle
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