Question on refraction of light

[daisyhur]

Homework Statement

under what condition is the angle of incidence greater than the angle
of refraction?and viseversa?
and WHY?

AND how come the speed of light slows down when it travels from a
less dense to a more dense substance?and vise versa?

Homework Equations

laws and principles of refraction and reflection

The Attempt at a Solution

i learned that When light ray enters a denser object, the ray bends and moves toward the normal and the angle of refraction is less than the angle of incidence.
but i still don't get WHY it is like that.
can anyone help me?

 

[cepheid]

The funny thing about optics is that it is possible to determine a lot about how light behaves without ever actually attempting to answer the question, "what is light?" In other words, in geometric optics or ray optics, we can describe how light propagates without understanding anything about its nature . This is satisfactory for many applications too. So the minimalist answer to your first WHY question is, "because light propagates in such a way that it obeys Snell's law." The question you will immediatly ask is then, why does Snell's law hold true? The answer is that Snell's law can be derived from a more general principle known as Fermat's principle, which describes what governs the path that light will take. A simplified statement of Fermat's principle is that light will take the shortest optical path between two points (where the optical path is determined not only by the distance between the points, but by how the refractive index changes along the way). Again, answering the question of WHY Fermat's principle holds requires a theory of light that is more advanced than geometric optics, one that actually attempts to answer the question of what light IS (e.g. electromagnetic optics, which models light theoretically as an electromagnetic wave. This is a pretty good model, in that it explains why light propagates the way it does in most cases).

However, there is an alternate, sort of "in between" approach that we can take that might offer you some more insight. Even before electromagnetic theory was developed, there was experimental evidence to suggest that light had wavelike properties. So Huygens was able to develop a "wave" picture of light that explained why it propagates the way it does, despite the fact that he didn't have any idea of what the *nature* of these waves were. He basically said that light propagates in a way analogous to water waves...the successive "wavefronts" can be constructed by assuming that every point on a preceding wave front emits a little "wavelet", and that these wavelets all combine together farther ahead to make the next wavefront. Although this has nothing to do with the physical picture of what light waves actually are, if you take it as a purely geometric method of constructing the light wavefronts, you will see that it is in agreement with how light actually propagates. So, in the image below, I've drawn a light wave (represented by flat green wavefronts in this case) incident on the interface between two media (the darker blue one is more dense). The normal to the interface is in black.

http://img54.imageshack.us/my.php?image=refractionem1.png

Now here is the key point: *if you are willing to accept it as a given that the wavefronts must travel more slowly once they cross into the denser medium*, then you can see that the wavefronts on the denser side are closer together (compressed), because they do not advance as far in the same amount of time as the wavefronts on the left side of the interface. However, if the wavefronts are also to remain continuous across the boundary, then the only way for this to be possible is if the wavefronts bend as shown. The greater the difference in the speed of the wavefronts between the two sides, the more bending occurs. The usual analogy is that you're driving on on pavement when the right side of your car hits a patch of sand. Since this slows down your right tires, but not your left tires, your car ends up swerving to the right (your car's path is bent).

Now, the usual way to reconcile this wave picture of light with the ray picture is to assume that the light "ray" is a line perpendicular to the wavefronts, and therefore represents their direction of propagation. This ray is shown in yellow, and it bends as expected due to the bending of the wavefronts.

This answers your first question, but not your second. I.e. in this explanation, I asked you to take it on faith that the wavefronts must advance more slowly on the side that is more optically dense. Again, to really answer the question of WHY that is the case, we must appeal to a more advanced theory of light, one that attempts to explain its nature. Before such theories were developed, the best answer people could give was "because it has been observed experimentally to be true." Nevertheless, I hope this diagram and explanation makes refraction a little more understandable.

 

[cepheid]

I thought I'd attach the image too, in case imageshack deletes it.