Optics Series Lecture, Lecture – XI.
“Fresnel’s Bi-prism: measurement of wavelength of light by it.” This lecture was delivered on 16th February in a lecture session of 1 and 1/2 hours. This lecture was delivered to Physics elective students and later to honors students. This web-version does not strictly pertain to 1 and 1/2 hours of regular lecturing session that we have mostly been employing.
That’s because it was created with another part which can be optionally appended to other related subject matter. In this web-version that’s what we will do. Our guiding principle is more in line with the honors course, where the subject matter is quite extensive and deep which brings more flexibility and choices into the lecture compositions.
Today we will discuss another interesting interference set-up, now that we have discussed the Young’s double slit experiment, in lecture – IX. A few words about the general mechanism behind interference. There are two kinds of interference basically that we will be discussing in our lectures. We discussed the Young’s DS interference pattern based on our understandings of intensity or irradiance patterns that we studied here: lecture – VII.
Interference is sustained and visible if the corresponding sources of light are coherent among themselves, that is, if the sources have phase differences that are not arbitrarily or abruptly changing, as a consequence we can safely assume the phase differences are constant and therefore predictable. Incoherent light makes this impossible.
Incoherent light is that light source whose production itself is arbitrary and abrupt and unpredictable, hence nothing can be definitively said on its phase, as a result the coherence is only short lived. If two light sources are so generated that their respective coherence time (or coherence length) are well within each others span, they are said to be coherent light.
Recall the idea of temporal and spatial coherence here that we discussed: here, when we discussed Young’s DS interference. We observe one basic thing about interference here. The two coherent sources S1 and S2 that we considered give rise to two different wave-fronts that meet up after traversing their respective optical paths. When they meet they produce interference. For this reason such type of interference are called as wave-front splitting interference.
Young’s DS experiment is an example of wave-front splitting interference. The Fresnel bi-prism that we will discuss is also an example of wave-front splitting interference. But there is yet another type of interference mechanism. Its called amplitude-splitting interference, examples of which are colors of thin films and Newton’s ring phenomena which we will study soon enough in future lectures.
In an amplitude splitting interference what happens is there is only one wave (or its wave-fronts) which splits into different components such as reflected or transmitted (refracted) parts according to the respective coefficients for these processes. So the amplitude has a fraction which is reflected and another which is refracted.
Naturally the question of coherence does not deter the production of interference effects. There always is inherent coherence in the amplitude splitting processes. When these different components meet up later, they produce interference.