Interference of light (Introduction)
An important characteristic of light waves is their ability, under certain circumstances, to interfere with one another. Most people observe some type of optical interference every day but do not realize what is occurring to produce this phenomenon. One of the best examples of interference is demonstrated by the light reflected from a film of oil floating on water. Another example is the soap bubble that reflects a variety of beautiful colours when illuminated by natural or artificial light sources. We will see the reason for all in this chapter. So here we are going to discuss the topic Interference of light.
COHERENT SOURCE
Two sources of light that emit continuous light waves of the same frequency, same wavelength, and have constant phase difference at all times are called coherent sources.
Here above fig shows some methods to obtained two coherent source s1 and s2.
NOTE:-
Two incoherent sources of light cannot produce an interference pattern.
SUPERPOSITION PRINCIPLE
The superposition principle state that when two or more waves travelling through a medium, superimpose on one another, a new wave is formed which has a resultant displacement at any instant equal to the vector sum of the displacements due to individual waves at that instant.
i.e
where are the function of time and space
INTERFERENCE OF LIGHT WAVE
The phenomenon of redistribution of light energy in a medium as a resultant of the superposition of light waves from two coherent sources is called interference.
Note that light waves interfering must have the same amplitude, otherwise the resulting interference pattern will lack contrast.
If the two waves are in phase, the amplitude of the resultant wave is equal to the sum of the amplitude of the two waves. This is called constructive interference.
If the two waves differ in phase by , the resultant wave amplitude is the difference between the amplitude of the two waves. This is called destructive interference.
If the amplitude of two waves is same then, in constructive interference resultant amplitude is double and in destructive interference, the resultant amplitude is zero.
We know that the Intensity(Energy) of a wave at any point is directly proportional to the square of its amplitude.
i.e At constructive interference, the resultant intensity is 4 times increases( Bright) and at destructive interference, the resultant intensity is zero(Dark)
ENERGY CONSERVATION IN INTERFERENCE OF LIGHT
Here the law of conservation of energy is obeyed. In the case of constructive interference, intensity becomes maximum and bright fringes are formed in the screen whereas in case of destructive interference, the intensity being minimum, dark fringes are formed. This implies that in interference and diffraction pattern, the intensity of light is simply being redistributed i.e. energy is only transferred from dark to bright fringe and no energy is created or destroyed in the process. i.e we can say that in interference phenomena, energy is conserved.
From fig, Path difference
It is clear from fig, if the path difference at p from two sources s1 and s2 is , then the phase difference of two waves originated from s1 and s2 must be
.
i.e for path difference , phase difference(
) is
for path difference 1, phase difference(
) is
for path difference
, phase difference(
) is
Consider two monochromatic coherent sources of light s1 and s2, emitting waves of wavelength . Let A be the amplitude of each wave and
is the angular frequency. Then the wave can be represented as
where is the phase difference at a point P
According to the superposition principle, the resultant displacement (y) at point p is
The amplitude of the resultant displacement is and therefore the resultant intensity at that point will be
Also
It is clear from the expression, the resultant intensity (I) at point P depends upon the phase difference () between the two waves reaching the point p.
for constructive interference, the resultant intensity will be maximum.
we know that
Hence Constructive interference will occur at any point P if the two waves arriving at P have a phase difference of an integral multiple of or path difference of an integral multiple of the wavelength
here
For destructive interference, the resultant intensity will be minimum.
similarly as above
here
NOTE:-
(1) All bright fringe have the same intensity
All Dark fringe have the same intensity
(2) If the two sources are coherent, then the phase difference at any point will not change with time and we will have a stable interference pattern: i.e the position of maxima and minima will not change with time. If two sources are incoherent, then the phase difference is not constant. i.e the position of maxima and minima will also vary with time and we will see the average intensity distribution. The Average intensity will be given by
(3) When two waves have different amplitudes:- If the two interfering waves have different amplitudes, say and
(
), then the magnitude of the amplitude R of the resultant wave is
we know that
i.e we can write
for constructive interference
for destructive interference
Also, we know that the intensity of light from a slit is directly proportional to the width of the slit. If W1 and W2 are the widths of two slits from which intensities of light I1 and I2 respectively, then
| Introduction | Huygens Principle |
| Refraction and Reflection of Plane waves using Huygens Principle | Coherent and Incoherent Addition of Waves |
| Interference of Light Waves and Young’s Experiment | Diffraction |
| Polarisation | |