Question

Two periodic waves of intensities I₂ and I₂ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

I₁ + I₂

$open parentheses square root of straight I subscript 1 end root plus square root of straight I subscript 2 end root close parentheses squared$
$left parenthesis square root of straight I subscript 1 end root minus square root of straight I subscript 2 end root right parenthesis squared$

2(I₁ +I₂)

Solution

2(I₁ +I₂)

Resultant intensity of two periodic waves is given by
$straight I space equals space straight I subscript 1 space plus space straight I subscript 2 space plus space 2 square root of straight I subscript 1 straight I subscript 2 end root space cosδ$
where δ is the phase difference between the waves. For minimum intensity
δ = 2nπ; n = 0,1,2,...... etc.
Therefore, for zero order maxima, cos δ =-1
$straight I subscript max space equals space straight I subscript 1 space plus straight I subscript 2 space plus space 2 square root of straight I subscript 1 straight I subscript 2 end root space equals space left parenthesis square root of straight I subscript 1 end root space plus space square root of straight I subscript 2 end root right parenthesis squared For space minimum space intensity comma space space equals space left parenthesis 2 straight n minus 1 right parenthesis straight pi semicolon straight n space equals space 1 comma 2 comma.... etc. Therefore space for space 1 space st space order space minima comma space cos space space equals space minus space 1 straight I subscript min space equals space straight I subscript 1 space plus space straight I subscript italic 2 space minus space 2 square root of straight I subscript 1 straight I subscript 2 end root left parenthesis square root of straight I subscript 1 end root space minus space square root of straight I subscript 2 end root right parenthesis squared therefore straight I subscript max space plus straight I subscript min space equals space space left parenthesis square root of straight I subscript 1 end root space plus space square root of straight I subscript 2 end root right parenthesis squared space plus left parenthesis square root of straight I subscript 1 end root space minus space square root of straight I subscript 2 end root right parenthesis squared equals space 2 space left parenthesis straight I subscript 1 space plus straight I subscript 2 right parenthesis$

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Wave Optics

Some More Questions From Wave Optics Chapter

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

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