Show that interference involves only redistribution of energy

Asked by Akshya Achu | 28th Sep, 2014, 10:07: AM

Expert Answer:

Interference of light is the phenomenon of re-distribution of light energy in a medium due to the superposition of light waves from two coherent sources.
Consider that two sources of light are emitting light waves of amplitude a1 and a2. If there is no interference between the light waves from the two sources, then the intensity of light at any point on the screen will be:
I = I1+ I2
We know that intensity is the square of amplitude hence we can write that:
I = a12+a22 ------------------(1)
If light from two sources interfere, then maxima and minima will be formed. The intensities of light at maxima and minima are given by :
begin mathsize 14px style straight I subscript max space equals open parentheses straight a subscript 1 plus straight a subscript 2 close parentheses squared space and straight I subscript min space equals open parentheses straight a subscript 1 minus straight a subscript 2 close parentheses squared Therefore space average space intensity space of space light space on space the space screen space due space to space interference space is space given space by : straight I subscript aver equals fraction numerator straight I subscript max plus straight I subscript min over denominator 2 end fraction equals fraction numerator open parentheses straight a subscript 1 plus straight a subscript 2 close parentheses squared plus open parentheses straight a subscript 1 minus straight a subscript 2 close parentheses squared over denominator 2 end fraction or bold space bold space bold I subscript bold a bold v bold e bold r end subscript bold space bold equals bold a subscript bold 1 to the power of bold 2 bold plus bold a subscript bold 2 to the power of bold 2 bold minus bold minus bold minus bold minus bold minus bold minus bold minus bold minus bold minus bold minus bold left parenthesis bold 2 bold right parenthesis end style
 
From (1) and (2) it follows that when the interference takes place, light energy which disappears at the regions of destructive interference  appears at the regions of 
constructive interference so that the averege intensity of light remains the same.
Or we can say that the intensity of light is simple being redistributed .No energy is being created or destroyed in the process.

Answered by Jyothi Nair | 29th Sep, 2014, 09:04: AM