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. `3I and 2I`
B. `4I and 5I`
C. `16I and 3I`
D. `25I and I`

Answer

D

Explanation

Here, `I_(1)=4I and I_(2)=9I`
`I_("max")+I_(1)=I_(2)sqrt(I_(1)I_(2))=4I+9I+2sqrt(4I xx 9I)`
`=13I+2xx6I=13I=12I rArr I_(m)=25I`
`and I_("min")=I_(1)+I_(2)-2sqrt(I_(1)I_(2))=4I+9I-2 sqrt(4I xx 9I)`
`=13I-2xx6I=13I-12I rArr I_("min")=I`