IIT JEE and NEET Physics @ Venkats Academy IIT-JEE and NEET Physics

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.

Power and Focal Length of a Lens

Refraction of Light Through Prism

Problems and Solutions on Refraction of Light Through Prism

Angular Dispersion and Dispersive Power

Problems on Angular Dispersion and Dispersive Power

Working of Human Eye and Simple Microscope

Working of Compound microscope

Working of a Galilean Telescope

Different Theories of Light and Their Analysis

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.