# young's double slit experiment - interferance and energy conservation

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## young's double slit experiment

Introduction

Thomas Young  is thought to be the scientist who has performed the double slit experiment in 1800. Double slit experiment is an experiment in which light is allowed to diffract through slits which produces fringes, or wave-like interference patterns on  opposite screen.

Thomas Young in 1803 showed that how a ray of light split into two pieces and how it produces a pattern of light and dark bands, corresponding to the places where the waves added together or cancelled out and vanished. It was the only experiment which laid the foundations for the understanding of dual nature of the light, as a wave and as a particle at the beginning of the 20th century.

#### First of all we should know , what is interference?  which is given below :

When there is a single source of light, the distribution of light energy in all the directions will be uniform. But, when we have a two coherent sources of light, emitting light waves of same amplitude, same frequency and in the same phase, then it should noted that the distribution of light energy doesn't remain uniform in all the directions.

At some points,  Where crest of one wave falls on the crest of the other wave, the resultant intensity of light is maximum and at other points, where the crest of one wave falls on the trough of the other wave, the resultant intensity of light is minimum. This kind of modification in the energy distribution of light is called the interference of light.

Thus in final mode we can say that the interference of light is the phenomenon of redistribution of light energy due to superposition of light waves from the two coherent sources.

At the point, where the resultant intensity of light is maximum, interference is said to be constructive and at points, where the resultant intensity of light is minimum, the interference is said to be destructive. young's double slit experiment

### young's double slit experiment:

Thomas Young, known among the famous scientists, demonstrated the phenomenon of interference by a simple experiment.

'S' denotes a narrow slit which is illuminated by a monochromatic source of light. The width of slit is about 1 mm.

At a suitable distance from the slit "S" ,There are two narrow slits denoted by 'A' and 'B' at a distance of about 0.5 mm apart. These two slits denoted by 'A' and 'B' are placed parallel to slit 'S'. There is also a screen placed at a large distance about 2 metre from the slits 'A' and  'B'. When we illuminate the slit 'S' , by a monochromatic source of light, what happens, Alternate sources of a dark and  bright bands appear on the screen. These bands are known as the interference bands or the interference fringes. The bands starts to disappear, when one of the slits 'A' or 'B' is closed.

### Young's double slit experiment

#### Explanation :

According to Huygen's Principle,  when slit 'S' is illuminated by a monochromatic source of light, it emits spherical wave- fronts , and also the slits 'A' and 'B' emits spherical wavelets. It should be noted that the full line semi circles represent the crests and the dotted line semi circles represent the troughs.

At points, where the crest of one wave falls on the crest of other wave, then the interference observed is constructive and hence at these points we observe Bright bands. There are points in the figure which represents the bright bands.

At points,  where crest of one wave falls on the trough of other wave, then the interference observed is said to be the destructive one and the resultant intensity of light is minimum and hence at these points, we observe dark bands. There are some points in the given figure which represents the dark bands.

From this experiment,  Thomas Young established the wave nature of light, by measuring the wavelength of light

Note:

It should be noted that if white light is used as a parent source of light 'S' then the central bright fringe is white.  This central white Fringe is surrounded by a few coloured fringes. Also, it should be noted that the fringe nearest to the central white coloured fringe is violet and the fringe farthest from the central white coloured fringe is red.

#### Interference and Energy conservation :

Suppose we have a two sources of light emitting light waves of intensity I₁ and I₂ respectively and having amplitude "a" and "b" respectively.

If there were no interference , then the resultant intensity  at each and every point on the screen will be ;

I = I₁ + I₂

But,  I₁  =  a²        and   I₂  =  b²

I = a² + b² ......................(X)

If there were interference , then at some points bright bands are seen and at other points dark bands are seen .

Hence,

Imax = (a+b)²......................(i)

and         Imin = (a+b)²....................(ii)

Average intensity of light in the interference pattern is given by;

⇒                            Iaverage   =    Imax+Imin /2

Iaverage  = (a+b)² + (a−b)²/2

Iaverage   =  a² + b² + 2ab + a² + b² − 2ab ∕ 2

Iaverage  =  2a² + 2b² /2

Iaverage  = 2(a² + b²) /2

Iaverage  =  a² + b² .........(Y)

Hence , total intensity of light remains same whether there is interference or not. In other words, we can also say that in the interference pattern, energy is being transferred from regions of destructive interference to the regions of the constructive interference. No energy is being created or destroyed. Hence, we can say that the law of conservation of energy is being obeyed in the process of interference of light .

Conclusion

This article provides you information related to young's double slit experiment and explains the formation of dark and bright bands .However, the article also explains you the concept of interference and it's energy conservation. By the end,   young's double slit experiment and interference concept is clear.

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