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What is the interference? What are the conditions of interference? Differentiate between path difference and phase difference.

Interference

Interference is a phenomenon in which two waves superpose and form a resultant wave which is greater or lower amplitude. Interference also refers that when two waves comes from the same source or coherent source (because they have same frequency) superimpose and form a constructive and destructive interference pattern.  The interference effects can be observed with all types of waves like light, radio, acoustic, surface water waves or matter waves.

Condition of Interference:

• The sources of the waves must be coherent, which means they emit identical waves with a constant phase difference means same wavelength and same time period
• The two sources of light should be very close to each other.
• The waves should be monochromatic – they should be of a single wavelength.

Constructive interference:

If a crest of a wave gathers a crest of another wave of the same frequency at the same point, or when the phase difference between the waves is a multiple of 2π or two waves superpose in same phase then the resultant wave has larger amplitude this is constructive interference and bright fringe obtain on the screen.

• The path difference between two waves is n lemda

d=n λ

or path difference = 0, λ, 2λ, 3λ….

where n = 0, 1,2,3…..

Destructive interference:

If a crest of one wave gathers a trough of another wave or when the difference is an odd multiple of π or two waves superpose in opposite phase then the resultant wave has minimum amplitude this is destructive interference and dark fringe obtain on the screen.

• The path difference between two waves is (n+1/2)lemda

d=(n+1/2)λ

or path difference = λ/2, 3λ/2, 5λ/2….

Where n = 0, 1,2,3…..

The phenomenon of interference may be grouped into two categories i.e. Inference by Division of Wavefront and Inference by division of amplitude.

• Division of Wavefront

Division of wavefront: In this method we obtain coherent sources with the help of dividing the wavefront which is originate from a common source.  In this class of interference requires essentially a narrow slit source.

For examples: Young Double slit experiments, Fresnel biprism experiments etc.

• Inference by division of amplitude

Division of Amplitude: When the amplitude of incident beam is divided into more than one fragment by partial reflection or refraction, this method is known as division of Amplitude method. The thin film inference is the best examples of division of Amplitude inference. With the help of division of amplitude we produce coherent beams; these beams travel different paths and are finally brought together to produce interference. The effects resulting from the superposition of two beams are referred to as two beam interference and those resulting from superposition of more than two beams are referred to as multiple beam interference.

For examples: Interference in thin films, Newton’s rings, and Michelson’s interferometer etc.