Test: Coherent & Incoherent Sources - JEE MCQ

To obtain well-defined interference patterns, the intensity at points corresponding to destructive interference must be zero, while intensity at the point corresponding to constructive interference must be maximum. To accomplish this the necessary condition is that the two interference sources must be coherent, that is, they must keep a constant phase difference.

When interference occurs with coherent sources, the amplitudes of the superimposing waves add like vectors. This means that the individual wave amplitudes combine based on both their magnitudes and directions (phases), which is a vector-like addition. The resulting intensity of the wave is proportional to the square of the total amplitude, but the addition of waves themselves is based on the vector sum of the amplitudes.

In physics, two wave sources are perfectly coherent if they have a constant phase difference and the same frequency (amplitude may be different).
As c be the speed of light which is constant.
Using, c=νλ
Now same ν gives same λ. for the two light sources.
Example: y₁​=A₁​sinwt  and y_2​=A₂​sin(wt+ϕ) where ϕ is constant.

Two sources are coherent if the waves they emit have the same wavelength and maintain a constant phase difference, ϕ. If the constant phase difference. ϕ, is zero, the two sources are said to be in phase.

Division of wave front where wave front is divided into two or more parts with the help of mirrors, lenses and prisms. The common methods are : Young's double slit arrangement, Fresnel's biprism method, Lloyd’s mirror method etc.
 
Division of amplitude where amplitude of the incoming beam is divided into two or more parts by partial reflection or refraction. These divided parts travel different paths and reunited later to produce interference. E.g. Newton's rings, Michelson’s interferometer etc.
 

When a light travels from one medium to another then deviation in the path of light known as refraction. And in the prism surrounding medium is air and material medium is glass due to the change of medium refraction will occur in prism.

Given, 
Frequency f=60kHz=60000Hz
Velocity of EM wane=v=3x108 m/s
Wavelength λ
We have v=f x λ
3x108 m/s= 60000 Hz x λ
λ=5000m
λ=5km
Destructive interference.

λ is the wavelength of light in air.

Let t be the distance between points S and A.

Optical path length travelled by light via SB

Optical path length travelled by light via SA = μt
Path difference between points  A and B
Now  phase difference

Hence,    

For sustainable interference wavelengths have to be the same. So frequency has to be the same too. Contact phase relation is also necessary to sustain the interference pattern else the pattern will keep changing so rapidly that we will not see any pattern.
Equal intensity is not a requirement to keep pattern sustained.

The correct answer is option D
In A,B,C there is a single source (coherent source)while in D there is an interference of thin films whose sources are different ,therefore not coherent.