Phase difference vs Path difference
Phase difference and path difference are two very important concepts in optics. These phenomena are seen on problems of wave model of light, which takes light as a travelling wave. Both, the path difference and phase difference are very important when it comes to explanation of phenomena such as Young’s double slit experiment, single slit diffraction, Newton’s rings, Thin film interference, Fresnel’s double mirror experiment, Fresnel diffraction, Diffraction gratings, and zone plates. These phenomena also have applications such as Cornu spiral and Fresnel biprism. In this article, we are going to discuss in depth what phase difference and path difference are, and their significance, applications and differences.
To understand phase difference one must first understand what “phase” is. A travelling wave can be defined using the equation Y(x) = A sin (ωt – kx) where Y(x) is the displacement on the y axis at point x, A is the amplitude of the wave, ω is the angular frequency of the wave, t is the time, k is the wave vector or sometimes referred as wave number, x is the value on the x axis. The phase of a wave can be interpreted in several ways. The most common one is that it is the (ωt – kx) part of the wave. It can be seen that at t=0 and x=0 the phase is also 0. ωt is the number of total revolutions the source of the wave have done when the time is t, (ωt – kx) is the total angle the source has turned. Phase difference is only useful when it comes to waves of the same frequency. The phase difference tells how much a wave is lagging or leading with respect to another wave. If two waves interfere and their phase difference is zero, the amplitude of the resulting wave is the addition of the two incident waves; if the phase difference is 180° or π radians, the result is the subtraction between the two amplitudes.
The path difference of two waves can be separated into two categories. The first one is the physical path difference and the second one is the optical path difference. The physical path difference is the measured difference between the two routes taken by the two waves. The optical path difference is the addition of each path element multiplied by the refractive index of the medium the path element is in. it can be mathematically denoted as the integral of n(x) dx.
What’s the difference between path difference and phase difference?
– Both the path difference and phase difference contribute equally to the displacement of the resultant wave.
– Path difference occurs due to the difference of the route taken and the refractive indices of the media in each route, while phase difference occurs mainly due to the phase inversion of waves when a hard reflection occurs.
– The path difference is measured in meters, whereas the phase difference is an angle which is measured either in radians or degrees.