Question

What are coherent sources? Why are they necessary for observing stable interference pattern? Draw a graph showing the variation of intensity of light with the position on the screen in Young’s double-slit experiment.

Hint:

For sustained interference: \[ \text{Coherent Sources} \Longrightarrow \text{Same Frequency + Constant Phase Difference} \] If the phase difference changes continuously, a stable interference pattern cannot be observed.

Answer 1

Concept: The phenomenon of interference is based on the principle of superposition of light waves. When two or more coherent light waves overlap, the resultant intensity at a point depends upon their phase difference. A stable interference pattern can be observed only when the phase difference between the interfering waves remains constant with time.

Step 1: Definition of coherent sources Two sources of light are said to be coherent if they emit light waves having:
• Same frequency (or wavelength),
• Constant phase difference,
• Nearly equal amplitudes. Thus, if the phase difference between the two waves is represented by \(\Delta\phi\), then \[ \Delta\phi=\text{constant} \] throughout the experiment.

Step 2: Necessity of coherent sources for stable interference pattern For a stable interference pattern, the positions of bright and dark fringes must remain fixed on the screen. If the sources are not coherent:
• Their phase difference changes randomly with time.
• The positions of maxima and minima continuously shift.
• Bright and dark fringes overlap each other.
• A clear and stable interference pattern cannot be obtained. Therefore, coherent sources are necessary because they maintain a constant phase difference and produce stationary bright and dark fringes on the screen.

Step 3: Intensity variation in Young's Double-Slit Experiment In Young's double-slit experiment, alternate bright and dark fringes are formed on the screen.
• Bright fringes correspond to constructive interference.
• Dark fringes correspond to destructive interference. The intensity varies periodically with position on the screen as shown below. Graph of Intensity versus Position on Screen

The maxima represent bright fringes while the minima represent dark fringes. Result: Coherent sources are sources having the same frequency and a constant phase difference. They are necessary for obtaining a stable interference pattern because only then the positions of bright and dark fringes remain fixed on the screen.