## Wednesday, January 28, 2015

### Interference of Light an Overview

The variation of intensity in the region of superimposition of two or more than two waves of same frequency with a constant phase difference is called interference.If two waves are met in such a way that the resultant intensity is maximum, then it is called constructive interference. This is possible when the two waves are met in the same phase.

If the two waves are met in such a way that the resultant intensity is minimum, then it is called destructive interference. This is possible when the two waves are met in the opposite phase.

For producing interference pattern of light, the two sources shall be coherent. Two sources are said to be coherent when there have a zero phase difference or a constant phase difference. Two different sources of light will never be coherent. We can get two coherent sources only when both the sources are drawn from a single source. A source and its image also can behave like coherent sources. The image can be a real image or it can be a virtual image.

An experiment is conducted to produce interference pattern and it is called Young’s double slit experiment. The light from a source is allowed to pass through two small slits. These two slits acts like coherent sources. They also behave like secondary sources with a constant phase difference. Hence they are qualified to produce interference pattern.

For interference pattern to appear on the screen, the distance between the slits and the screen shall be much larger than the distance between the slits.

We can draw a diagram to represent constructive interference and the destructive interference. When the two waves from the different sources are met in the same phase, the resultant intensity is maximum and they produce a bright spot. This is called constructive interference. When the two waves are met in the opposite phase, the resultant intensity is minimum and they produce a dark spot. This is called destructive interference. The central spot is a bright spot because by the time the two waves reach the point, there have zero phase difference.

To know the resultant intensity and the resultant amplitude at a particular point on the screen, we can draw the light from different sources at a point on the screen as shown. The two lights while reaching the point will experience a small path difference and hence there will be a constant phase difference also between them. They are represented in the diagram as shown below.

When the two waves are superimposed the resultant amplitude is different from the individual amplitudes and it also depends on the phase difference between the two waves. We can derive the equation for resultant amplitude and resultant intensity as shown below.

The formation of bright and dark fringes in interference pattern depends on how the two waves are met at a particular point. It can be proved mathematically that when the two waves are having a constant path difference that is equal to wavelength of the light, the resultant intensity is going to be maximum and that is called constructive interference. We can derive the equation for the constructive interference and the location of the bright spot on the screen as shown below.

The formation of the dark spot on the screen is possible when the two waves are met with a constant path difference of half of the wavelength. We can derive the condition as shown below.

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