Interference and analytical treatment of interference

 Q. Explain the term interference and give the analytical treatment of interference. 

Ans: Interference: When two or more than two waves travel in a medium then the modification in the intensity distribution in the region of superposition is called as interference. 

At the points where waves superpose with the same phase the intensity is maximum; and is called as constructive interference. While the points where waves superpose with the opposite phase the intensity is minimum; and is called as destructive interference. 

Types of Interference:

Interference can be classified on the basis of the way interference is produced. The interference is classified as:

1.Interference by Division of wavefront: When the incident wavefront is divided into two parts by the phenomenon of reflection refraction. When these two divided parts reunite then the interference obtained is called interference by division of wavefront. The examples are Fresnel bi prism, Lloyd’s mirror.

2.Interference by Division of amplitude: When the incident amplitude is divided into two parts by the phenomenon of reflection refraction. When these two divided amplitudes reunite then the interference obtained is called interference by division of amplitude. The examples are interference in thin films, Newton’s ring, and Michelson interferometer.

3.Analytical treatment of interference: Let us consider two plane waves in a medium in the same direction. The displacement of individual waves is given by y1& y2, while their amplitudes are a1& a2, the angular frequency of these waves is ‘ω’. Mathematically the waves can be 

represented as

𝑦1 = 𝑎1 sin 𝜔𝑡 1

𝑦2 = 𝑎2 sin(𝜔𝑡 + 𝜑) 2

Where 𝜑 is the phase difference between two waves.

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