Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

Options

A. 4 Iand I
B. 5 I and 3I
C. 9 I and I
D. 9 I and 3 I

Answer

C

Explanation

`I_("max")=a_(1)^(2)+a_(2)^(2)+2a_(1)a_(2)`
`=I+4I+2 sqrt(2Ixx4I)`
`= 9 I`
`I_("min")=a_(1)^(2)+a_(2)^(2)-2a_(1)a_(2)`
`=I+4 I-4I=I`