Understanding Interference of Light
Before we discuss interference of light, there are a number of basic terms in physics that you need to understand. In this edition, we will discuss the meaning of optical path and coherence.
Optical path
When a light travels a distance L in a medium of refractive index n, the optical path is nL.
The optical path in vacuum is L, since n = 1, for vacuum. The refractive index of air is 1.00 (to 3 significant figures). Therefore when light travels a distance L in air, the optical path equals the geometrical distance L.
When a beam travels a travel through a glass block of refractive index 1.5 and thickness d, the optical path would be 1.5d.
What would be the optical path when light travels a distance of 200 m in water of refractive index 1.33?
The answer is 266 m.
In the same time interval, the optical paths in different media are equal.
In air, the speed of light is represented by c, which is 3.00 108 m s-1. The speed of light in a medium of refractive index n is v =
The time taken for light to travel a distance L in air is t = L/c .
The distance travelled by light in a medium of refractive index n in time t = L/c is
l = vt = (c/n)(L/c )
Optical path in air L = nl, the optical path in the medium.
Not only the optical paths in different media are equal for the same time interval, but the numbers of complete wavelength in different media are also equal for the same time interval.
In the distance L in air, number of complete wavelength = L/wavelength .
In a medium of refractive index n, the wavelength of light = L/(wavelength inmedium) .
In the distance l in the medium,
number of complete wavelength = l/(wavelength inmedium)
= l/(wavelength/n)
= nl/wavelength (nl = L)
= L/wavelength
= number of complete wavelength in air.
Optical Path Difference
Optical path difference means the difference in the optical paths.
For example the optical path between two points X and Y in air separated by a distance L is L. When a glass block of refractive index n is placed between X and Y,
new optical path = optical in air + optical path in the glass block
= (L x) + nx
= L + (n -1)x which is greater.
The optical path difference = [L + (n -1)x] L
= (n -1)x
Coherence
The necessary condition for interference of waves is that the waves must be from two coherent sources. Two wave sources are coherent if there is a constant phase difference
between the sources. Constant phase difference means that the phase difference does not change with time. For this to happen, the waves from the two coherent sources must have the same frequency.
Examples of waves from coherent sources are shown below.
(a) The two waves A and B are in phase because their peaks occur at the same instant.
Phase difference = 0 degree and is constant
(b) The two waves P and Q are in anti-phase.
Phase difference = 180 degrees and is constant
(c) The distance between the peaks of the two waves X and Y = 1/4 of a wavelength,
which is equivalent to a phase difference of 90 degreees.
