Interference of Waves | Superposition and Interference in light and water waves | Physics

Interference of Waves | Interference and superposition explained in light and water waves with animation | Interference of waves in two dimensions | Physics

The phenomena of the light which undergoes refraction and reflection by be explained by the 2 theories of light. They are corpuscular and wave theory of light. But some of the other phenomena such as interference and diffraction can only be explained by wave theory of light.
We know that 2 or more wave, motions travel in space at the same time. Sometimes these 2 wave motions combine to and some physical effects take place. Inference is once such physical effect.
When 2 or more waves cross each other in the same medium, they both interfere and accident takes. This accident is known as interference of waves. Interference is the combine effect of the disturbance caused by the each individual wave at the same place and at same time. This effect can be understood from the principle of superposition of waves.
Principle Of superposition of waves:
To understand this concept of the superposition, let's understand some of the examples. When we drop a pin in a tank, we see some circular waves. When other another pin is dropped, we see some more waves. These waves travel in the same tank and some or the other time these superimpose on each other. The resultant wave would have amplitude which is the sum of the displacement due to the individual waves.
" The principle of superposition of waves states that when two or more waves travel through the same medium simultaneously, the resultant displacement at any point is the vector sum if the displacement due to the individual waves."
In our case the pin is dropped in a ripple tank with 2 pins. If Y1 is the displacement caused at a point due to the first source and Y2 is the displace cause by the 2nd source, then the over displacement R at the point of interference would given by
R=Y1+Y2
When both the sources have the same amplitude which then Y1,Y 2 would be equal to Y. When Y1 is due the crest or trough and Y2 is also due a crest or trough the resultant would be the maximum and when Y1 is due to a crest and Y2 is due to a trough or vice versa, the displacement would be minimum.
When maximum displacement takes place it's called constructive superposition and when minimum displacement takes place it's called the destructive superposition. In constructive displacement, a maximum displacement curve is produced. Thus, when constructive displacement occurs then the phase difference between the waves would be ZERO or a multiple of 2π.
When minimum displacement occurs, wave super impose destructively, the phase difference of the waves would be π or an odd integral multiple of the π.
Interference of waves:
When superposition of waves occurs, they could be constructive or destructive. This physical effort observed as a result of the superposition of waves is called interference.
"The physical effect of the superposition of waves from the sources vibrating with the same frequency and amplitude is called the interference of waves. The physical effect is in the form of vibrations in the amplitude of resultant wave in a given potion of the medium"
Interference is a special case of superposition of waves which originate from different sources but have the same amplitude, same frequency.