Question

Explain, using phasor diagrams, why each statement is true. (a) A minimum occurs whenever ϕ is an integral multiple of 2π/N, except when ϕ is an integral multiple of 2π (which gives a principal maximum). (b) There are (N-1) minima between each pair of principal maxima.

Short answer

The ϕ = 2nπ is a principal-maxima and there will be n-1 minima.

Step-by-step solution

Given Data

Diffraction is a process by which a beam of light spreads when passing through a narrow passage or across the edge of an obstacle accompanied by interference between the waveforms.

Reason for statements

The phasor for the above can be represented as:

It can be seen that for ϕ = 2nπ, multiplication of waves occurs with same phase which means there will be a single principal maxima.

Also, if n-slits are available then there will be n different phases, and excluding the one that is 2nπ, it is evident to get n-1 minima.

Therefore, the ϕ = 2nπ is a principal-maxima and there will be n-1 minima.