Interference of Light Waves and Young’s Experiment

Suppose you are busy studying in your room and one of your friends calls you out for cricket. So what happens here is that he has interfered you with what you were doing. So that was kind of disturbance for you. Let us now study about something called as an interference of light waves.

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Constructive and Destructive Interference of Light Waves

We know that there are two kinds of interference of light waves, which are:

• Constructive Interference:  Suppose if the crest of one wave falls on the crest of another wave, then the amplitude is maximum. This is constructive interference. Here both the waves have the same displacement and the waves are in phase.
• Destructive interference: Suppose if the crest of one wave falls on the trough of another wave, then the amplitude here is minimum. This is destructive interference. Here the waves do not have the same displacement and the waves are out of phase.

Download Wave Optics Cheat Sheet by clicking on the button below

Browse more Topics under Wave Optics

• Coherent and Incoherent Addition of Waves
• Diffraction
• Huygens Principle
• Polarisation
• Refraction and Reflection of Plane Waves using Huygens Principle

Condition of a Steady Interference Pattern

1. A_{1 =} A_{2 .} The amplitude of two waves must be equal.
2.  λ_{1 =} λ_2. The two waves interfering must have same color i.e they must be of the same wavelength.
3. Sources must be narrow.
4. The distance between source should be less.
5. Source and screen should be at large distance.
6. We should get coherent sources.

Path difference for constructive and destructive interference

Suppose there are two coherent sources S₁ and S₂. There is also a point source P. The point source P is located at the same distance from the sources  S₁ and S₂. When both the sources are in the same phase, the constructive path difference will be 0, λ, 2λ……. The destructive path difference will be λ/2, 3λ/2, 5λ/2……

Young’s experiment

Young’s performed an experiment to prove the wave nature of light by explaining the phenomenon of interference. He used two coherent sources to perform in this experiment. He used a light bulb and two small slits, S₁ and S₂ and source S.

Here in the above figure, we can see that the slits are placed very close to each other and are separated by the distance ‘ d ‘. There is a screen placed in front of this setup. He observed that alternate dark and light bands were formed on the screen. Why did this kind of pattern come on the screen?

The source S illuminate the source S₁ and S_{2 .}Therefore the light from S₁ and S₂ becomes coherent. Why did they become coherent? This is because both S₁ and S₂ receive their light from the same source S. So if there is any change in the phase, the change will reflect in both S₁ and S₂. When both the slits are open fringes are formed.

Suppose you have two taps in your house and water that comes in both the taps is coming from both the source. So if you put some mud at the source of the water, the moment you open the taps, you will see that water from both the taps will be muddy. Whatever changes you make in the source, the same changes are seen in the taps too.

∴  we can say that S₁ and S₂ will always remain in phase.

In the double-slit experiment consecutive bright as well as dark fringes are seen on the screen as a consequence of the type of interference of light waves.

• The interference fringe maxima occur for path difference = n λ
• The interference fringe minima occur for path difference = (2n+1) λ

Solved Question For You

Q. A YDSE uses a monochromatic source. The shape of the fringe formed on the screen is

1. Hyperbola
2. Circle
3. Straight line
4. Parabola

Answer: C. If the light consisted of ordinary particles, and these particles were fired in the straight line through the slit and allowed to strike a screen, we would expect to see a pattern of the size and shape of the slit. Here the shape of the fringe forms on the screen is the straight line.