Why is the bending of waves related to wavelength?

In summary, the bending of waves, also known as diffraction, occurs when a wavefront is truncated or passes through an aperture. The amount of bending depends on the ratio of the wavelength and the size of the aperture. This phenomenon is related to the invariance of scale, where halving the wavelength without halving the aperture size produces the same diffraction as doubling the aperture size without changing the wavelength. It is important to note that surface waves in a ripple tank and electromagnetic waves behave differently, despite both being waves.
  • #1
triac
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Why is the "bending" of waves related to wavelength?

Hi!
As stated in the title, my question concerns the "bending" of waves. (I'm quite sure that "bending" is not the proper term, so if you know the correct one, please tell me.)
Let's say that we investigate waves in a ripple tank. We create a plane wave and put a blockage, parallell to the wavefront, with a small slit in it. If the slit is small enough, we will get almost circular waves on the other side of the blockage, but if the slit is large, the wave on the other side will not be as much bent. This seems natural to me, but I don't understand how it is related to wavelength. My questions are:

1. In our physics textbook, there was an inequality for "bending" of waves in an experiment like the one described above: D[tex]\leq[/tex][tex]\lambda[/tex], where D is the width of the slit and lambda is the wavelength. What do they mean by this? The bending of the waves gets less and less, the wider the slit is, but it never disappears. How then, can you give such a condition for "bending".

2. Why does the wavelength affect the "bending" of the waves?

Thanks in advance!
 
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  • #2


1. The condition you describe is where you get the diffracted wave propagating through 180 degrees; it only occurs when the width of the slit is comparable to (or less than) the wavelength/2. At wider slit widths, "bending" still occurs, just not through the whole 180 degrees.

2. It is due to the invariance of scale, which basically says that if you halve the wavelength and halve the aperture size, the wave diffracts in exactly the same way. If you halve the wavelength without halving the aperture size, this is equivalent to doubling the aperture size without changing the wavelength. To summarise, the wavelength matters, because the diffraction you get depends on the ratio of the wavelength to the aperture size, not just the wavelength.

Claude.
 
  • #3


As Claude states, you are talking about *diffraction*. The origin of diffraction is truncating a wavefront. Perhaps you have seen Huyghens' principle: each point on a wavefront can be considered a source point, which will radiate in all directions.

So, how to construct a flat wavefront? That occurs when all the different source points interfere in such a way that the total wavefront is a flat surface, and this can only occur if the wavefront is infinitely large (or, the original point source is infinitely far away). So, by truncating the flat wavefront (by passing through an aperture, for example), the small piece of wavefront diffracts outward ('spreads', 'curves', 'bends'..), and the rate at which it diffracts is related to the ratio of the wavelength and size of aperture. Even if the aperture is much larger than a wavelength, if the wavefront is not a complete sphere, there will be diffraction.

One small note of caution: surface waves, in a ripple tank, are significantly different that electromagnetic waves- both are waves, but that's the only real similarity.
 

1. Why do waves bend when they encounter different mediums?

Waves bend when they encounter different mediums because of a phenomenon called refraction. When waves travel from one medium to another, their speed and direction change, causing them to bend.

2. How does the wavelength of a wave affect its bending?

The wavelength of a wave determines the amount of bending when it encounters a different medium. Longer wavelengths experience less bending, while shorter wavelengths experience more bending.

3. What role does the speed of the wave play in its bending?

The speed of the wave is directly related to its wavelength and frequency. The speed of a wave changes when it enters a different medium, which causes the wave to bend.

4. Can the angle of incidence affect the bending of a wave?

Yes, the angle of incidence, which is the angle at which the wave enters the new medium, can affect the bending of a wave. As the angle of incidence changes, the amount of bending also changes.

5. How is the bending of waves related to the properties of the medium?

The bending of waves is related to the properties of the medium, such as its density and composition. These properties determine how much the speed of the wave changes, which in turn affects the amount of bending.

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