Consistent sources and prolonged light interference:

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Two sources of light waves are said to be coherent if the initial phase difference , between the waves emitted by the sources remains constant in time. If ยง, changes randomly with time, the sources are called incoherent. Two waves produce interference pattern only if, they originate from coherent sources. This condition is same as discussed for sound waves.

The process of light emission from ordinary sources such as the sun, a candle, an electric bulb etc. is such that one has to use special techniques to get coherent sources. In an ordinary source, light is emitted by atoms in descrete steps. An atom after emitting a short light pulse becomes inactive for some time. It again gains energy by some interaction, becomes active and emits another pulse of light. Thus, at a particular time a particular group of atoms is active and the rest are inactive. The active time is of the order of 108 s and during this period, a wavetrain of several meters is emitted.

We can picture the light coming from an ordinary source as a collection of several wavetrains, each several meters long and having no fixed phase relation with each other. Such a source is incoherent in itself.

Different wavetrains are emitted by different groups of atoms and these groups act independently of each other, hence the phase varies randomly from train to train. If two lamps are substituted in place of the slits S, and S, in a Young’s interference experiment, no fringe will be seen. This is because each source keeps on changing its phase randomly and hence, the phase difference between the two sources also changes randomly. That is why, a narrow aperture S, is used to select a particular wavetrain which is incident on the two slits together. This. ensures that the initial phase difference of the wavelets originating from S, and S, does not change with time. When a new wavetrain is emitted by the lamp, the phase is randomly changed but that change is simultaneously communicated to both S, and S, and the phase difference remains unchanged. In order to obtain a fairly distinct interference pattern, the path difference between the two waves originating from coherent sources should be kept small. This is so because-the wavetrains are finite in length and hence with large difference in path, the waves do not overlap at the same instant in the same region of space. The second wavetrain arrives well after the first train has already passed and hence, no interference takes place. In practice, the path difference should not exceed a few centimeters to observe a good interference pattern.

Because of the incoherent nature of the basic process of light emission in ordinary sources, these sources cannot emit highly monochromatic light. A strictly monochromatic light, having a well defined single frequency or wavelength, must be a sine wave which has an infinite extension. A wavetrain of finite length may be described by the superposition of a number of extensores of different wavelengths. Thus, the light emitted by an ordinary source always has a spread in wavelength. An ordinary sodium vapour lamp emits light of wavelength 589.0 nm and 589.6 nm with a spread of about 0.01 nm in each line. Shorter the length of the wavetrain, larger is the spread in wavelength.

It has been made possible to produce light sources which emit very long wavetrains, of the order of several hundred metres. The spread in wavelength is accordingly very small. These sources are called laser sources. The atoms behave in a cooperative manner in such a source and hence the light is coherent. Two independent laser sources can produce interference fringes and the path difference may be several metres long.

9. DIFFRACTION OF LIGHT :

The phenomena of bending of light around the corners of an obstacle or an aperture into the region of geometrical shadow is called diffraction of light. The diffraction is more pronounced when the dimensions of the obstacle/aperture is comparable to the wavelength of the wave.

TYPES OF DIFFRACTION:

Diffraction phenomenon can be divided into two classes :

Fresnel Diffraction: In this class of diffraction, the source or the screen or both are at finite distances from the obstacle or the aperture causing the diffraction as given in figure(A The phenomenon of diffraction obtained on the screen is known as Fresnel diffraction pattern Examples: Diffraction at a straight edge, small opaque disc, narrow wire are examples of

IMAGE OF FORMATION AND ACCOMMODATION :

The lens is hard in the middle and gradually becomes soft towards the outer edge. The curvature of the lens may be altered by the ciliary muscles to which it is attached. The light entering the eye forms an image on the retina Which covers the inside of the rear part of the eyeball. The retina contains about 125 million receptors called rods and cones which receive the light signal and about one million optic-nerve fibres which transmit the information to the brain. The space between the lens and the retina is filled with another liquid called the vitreous humor.

The cornea-lens-fluid system is equivalent to a single converging lens whose focal length may be adjusted by the ciliary muscles. Now onwards, we shall use the word eye-lens to mean this equivalent lens.

When the eye is focused on a distant object,

, the ciliary muscles are relaxed so that the focal

length of the eye-lens has its maximum value which is equal to its distance from the retina.

The parallel rays coming into the eye are then focused on the retina and we see the object clearly.

When the eye is focused on a closer object, the ciliary muscles are strained and the focal length of the eye-lens decreases. The ciliary muscles adjust the focal length in such a way that the image is again formed on the retina and we see the object clearly. This process of adjusting focal length is called accommodation. However, the muscles cannot be strained beyond a limit and hence, if the object is brought too close to the eye; the focal length cannot be adjusted to form the image on the retina. Thus, there is a minimum distance for the clear vision of an object.

Fraunhoffer diffraction : In the Fraunhoffer diffraction, the source and the screen are al

infinite distanes from the obstacle or the aperture causing the diffraction IPigure(B). In

this case, the light from the source at infinity after diffraction is focussed on the screen using the convex lens.

The phenomenon of diffraction obtained on the screen is known as Fraunhoffer diffraction

Fixamples: Diffraction at single slit, double slit and’ diffraction grating are the examples o Fraunhoffer diffraction.

10. DIFFRACTION OF LIGHT AT A SINGLE SLIT :

Light from mono-chromatic source of light S is made parallel after refraction through a len-L,. The refracted light from L, is propagated in the form of plane wavefront WW. The plane wavefront WW is incident on the slit A of width ‘d. According to Huygen’s

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