Reflection of Water Waves
Reflection of straight wavefronts at a plane surface
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Note: Both incident and reflected wavefronts are straight and have equal spacings.
The incident and reflected waves have the same speed and wavelength.
Reflection of Circular Wavefronts at Plane Surfaces
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Note: The source O corresponds to the object and the virtual source I of the reflected waves corresponds to the virtual image formed by a plane mirror.
Refraction of Water Waves
Water waves change direction (bend) when they travel across a boundary between deep and shallow water at a non-zero angle to the boundary.
This change of direction or bending is called refraction.
Refraction is observed as a result of a change in speed as waves move from deep to shallow water or vice versa.
Waves travel faster in deep water than in shallow water.
Refraction of straight wavefronts at a plane boundary
Medium 1 – incident-straight wavefronts in deep water
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i = angle of incidence
r = angle of refraction
Medium 2 – refracted straight wavefronts in shallow water
The above diagram shows that the waves travel more slowly in shallow water.
The wavelength changes (decreases) but the frequency does not as the frequency of the wave is a property of the source, not the medium.
By using the wave equation,
v =fλ, we may write: speed of waves in medium 1 (deep water) v1 = f x wavelength in medium 1 (λ1)
v1 = fλ1 … (i)
speed of waves in medium 2 (shallow water) v2 = f x wavelength in medium 2 (λ2)
v2 = fλ2 … (ii)
v1/v2 = λ1/λ2 è v1/ λ1 = v2/λ2
The refractive index (n) is a measure of the degree of refraction or bending which takes place when a wave passes from one medium into another. The refractive index is numerically equal to the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r). That is:
Refractive index (from medium 1 to medium 2) = sin (angle of incidence) (medium1)/sin (angle of refraction) (medium2)
1n2 = (sin i)/ (sin r)
The extent to which a wave is refracted depends on both the medium the wave is leaving and the medium it is entering. The relationship between refractive index (r) and the speeds (c1 and c2) and wavelengths (λ1 and λ2) in media 1 and 2, respectively, are:
1n2 = (sin i)/ (sin r) = v1/v2 =
1n2 = v1/v2
That is, the refractive index for a wave travelling from medium 1 to medium 2 is equal to the ratio of the speed of the wave in the two media:
Recall: v = fλ è v1/v2 = fλ1/fλ2
This shows that 1n2 = λ1/λ2