Two periodic waves of intensities `I_1` and `I_2` pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Options

A. (a) `I_1+I_2`
B. (b) `(sqrt(I_1)+sqrt(I_2))^2`
C. (c) `(sqrt(I_1)-sqrt(I_2))^2`
D. (d) `2(I_1+I_2)`

Answer

D

Explanation

Resultant intensity of two periodic waves is given by
`I=I_1+I_2+2sqrt(I_1+I_2)cos delta`
where `delta` is the phase difference between the waves.
For maximum intensity,
`delta=2nlambda, n=0, 1, 2, ….`etc.
Therefore, for zero order maxima, `cos delta=1`
`I_(max)=I_1+I_2+2sqrt(I_1+I_2)=(sqrtI_1+I_2)^2`
For minimum intensity, `delta=(2n=1)delta`,
`n=1, 2, ....` etc.
Therefore, for Ist order minima `cos delta=-1`
`I_(min)=I_1+I_2-2sqrt(I_1I_2)`
`=(sqrtI_1-sqrtI_2)^2`
Therefore,
`I_(max)+I_(min)=(sqrt(I_1)+sqrt(I_2))^2+(I_1-sqrt(I_2))^2`