# Refraction -- frequency remaining constant

#### logearav

Joined Aug 19, 2011
243
Revered Members,
When light travels from rarer to denser medium and vice versa, velocity and wavelength changes but frequency remains constant. What is the reason? This question was asked in the physics quiz competition held in my school. I replied that since energy of the light remains the same and since energy is proportional to frequency, frequency remains constant. But the convener said the answer is wrong. Am i wrong?

#### steveb

Joined Jul 3, 2008
2,436
It was a good try, and probably could be considered correct from some people's points of view. I think the problem with that answer is that our formula that relates energy and frequency must have built into it the fact that the frequency does not change, since that is what happens. If we lived in a crazy world where frequency did not remain the same but the energy did, then our formula that relates energy and frequency would reflect this fact.

For example, not only is $$E=h\nu$$ where E is energy, h is Plank's constant and nu is frequency, but it is also true that $$E={{hc}\over{\lambda}}$$, where c is the speed of light and lambda is the wavelength. Note the fact that the ratio of speed and wavelength remain the same when energy remains the same. Again, the formula reflects the fact, but does not explain it.

Often physics describes things more than it explains things, and the above is an example of that. But, this question allows an answer that is closer to being a real explanation. The usual explanation is that the wave must be connected at the boundary, so the up and down variations must match each other on each side, hence the fundamental frequency must be the same. This answer is more intuitive and easier to visualize. The case of light is not really up and down motion, so I say that figuratively. However, the field variations must match in particular ways at the boundary.

There is a subtlety to this answer. Note that above I said the "fundamental" frequency. If the media are linear (and the wave is a sinewave), then the fundamental frequency will be the only frequency. But, a nonlinear medium can generate harmonics which are multiples of the fundamental frequency.

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#### logearav

Joined Aug 19, 2011
243
The usual explanation is that the wave must be connected at the boundary, so the up and down variations must match each other on each side, hence the fundamental frequency must be the same. This answer is more intuitive and easier to visualize. The case of light is not really up and down motion, so I say that figuratively. However, the field variations must match in particular ways at the boundary.

Thanks a lot steveb. I can't understand what is up and down variations. Are you meaning crests and troughs?

#### steveb

Joined Jul 3, 2008
2,436
Thanks a lot steveb. I can't understand what is up and down variations. Are you meaning crests and troughs?
Yes, I think that captures the meaning. As I mentioned I said up and down in a figurative sense to draw an analogy with, for example, surface waves on the ocean. Light waves don't go up and down, but the fields vary in time in a crest and though kind of way. The boundary conditions at the interface between two media force the crests and troughs to match up physically. The wave speed and wavelength can change in the new medium, but the source of the wave is the boundary condition, and that source frequency is driven by the other side's frequency, due to the boundary condition.

So anyway, even though your answer is quite reasonable and respectable, this other answer is the one most people accept as being more fundamental and intuitive.

#### logearav

Joined Aug 19, 2011
243
The source of the wave is the boundary condition, and that source frequency is driven by the other side's frequency
steveb, Boundary conditions are constraints imposed on the probability of wave existence, I infer. So, what exactly you mean by source of the wave is the boundary condition.

#### steveb

Joined Jul 3, 2008
2,436
steveb, Boundary conditions are constraints imposed on the probability of wave existence, I infer. So, what exactly you mean by source of the wave is the boundary condition.
Well, this is a point of view one can take, and if it causes you any confusion, then don't worry too much about it. But, if you are curious, the answer is as follows.

When one considers Maxwell's equations (or other similar theories) we find that the fields are generally the result of sources. In electromagnetics, the two types of sources are charges and currents. The existence of charges and currents result in the fields.

However, often we solve problems that have no charge or current sources, and one has to wonder, "how did the fields come into being without the specification of a type of source?". The answer is that if we don't have a source, then we have a boundary condition which tells us the incoming fields (at the boundary) that generates the fields we are interested in. In a sense, the boundary condition is the source when we take an isolated view of our system. In reality, the fields at the boundary are the result of real current and/or charge sources that exist somewhere else in the universe, but we decide not to care about those details, since the boundary conditions tell us all we need to know about how those unknown sources affect the region of space we are interested in.