Two beams of light of intensity `I_(1), and I_(2)`interfere to give an interference pattern. If the ratio of maximum intensity to that of minimum intensity is `(16)/(4)` then `I_(1):I_(2)=` .......

Options

A. `1:9`
B. `4:1`
C. `1:4`
D. `9:1`

Answer

D

Explanation

`(I_(max))/(I_(min))=((a_(1)+a_(2))/(a_(1)-a_(2)))^(2)`
`(16)/(4)=((a_(1)+a_(2))/(a_(1)-a_(2)))^(2)`
`=2(a_(1)+a_(2))/(a_(1)-a_(2))^(2)`
`2a_(1)-2a_(2)=a_(1)+a_(2)`
`:.a_(1)=3a_(2)`
`:.(a_(1))/(a_(2))=(3)/(1)`
`:.(a_(1)^(2))/(a_(2)^(2))=(9)/(1)`
`:.(I_(1))/(I_(2))=(9)/(1) " " [ a_(1)^(2) prop I_(1),a_(2)^(2) prop I_(2)`Taking K=1 in both]