## Wednesday, January 28, 2015

### Representation of Light as Wave

Representation of the light as a wave

We can consider the light travelling like a wave. The particles of the medium through which the light is passing experience a displacement and it can be represented as shown below. Even before the oscillation starts the particles can have some displacement and it is called as initial phase. The position of the particle with respect to the mean position is called phase. The wave moving along the positive direction and the wave moving along the negative direction are shown with a different signs as shown below. We have also derived a small relation between phase difference and path difference.

We also know that velocity of the wave is the product of frequency of the wave with its wavelength. We shall understand that the velocity of the particle is different from the velocity of the wave.

The intensity of the light at any point is directly proportional to Squire of the amplitude.

Principle of superposition

When two waves are superimposed one over each other, the resultant of displacement is going to be different from individual displacements.

Treating the displacement as a vector, we can calculate the resultant amplitude as shown below. The derivation is made basing on the parallelogram law of vectors. It is clear from the derivation that the maximum possible amplitude of the two waves is equal to sum of the individual waves amplitudes. The minimum possible amplitude of the resultant wave is equal to the difference between the amplitudes of the two waves.

We can calculate the ratio of maximum amplitude to minimum amplitude as shown below. As we know that the intensity is directly proportional to Squire of amplitude we can also calculate the ratio of maximum intensity to minimum intensity.

Doppler effect of light

The apparent change in the frequency due to the relative motion is called Doppler effect. The change in the apparent frequency is not dependent of change in the velocity of the observer. It is simply because when compared with the velocity of the light, the velocity of the observer is significantly small. Therefore the impact of motion of the observer is less on the apparent change in the frequency of light.

We can explain the concept of blue shift and the red shift basing on Doppler Effect of light. When an astronomical body is approaching the earth, its apparent frequency increases. We know that the wavelength is reciprocal of frequency. As the frequency of the approaching body is increasing, its wavelength decreases. Among all the visible colors, violet is having the least possible wavelength but it is not a primary color. As the closest color with the dominating wavelength is blue, the body approaching the earth appears in blue color.

If an astronomical body is going away from the earth, its wavelength increases and it appears like red in color. This is called the red shift of the star.

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