In young double slit experiment the ratio of intentsities of bright and dark bands is 16 which means

Options

A. the ratio of their amplitudes is 5
B. intensities of individual sources are 25 and 9 units respectively.
C. the ratio of their amplitudes is 4
D. intensities of individual sources are 4 and 3 units respectively.

Answer

B

Explanation

`(I_("max"))/(I_("min"))=(16)/(1)=((sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))-sqrt(I_(2))))^(2)=((a_(1)+a_(2))/(a_(1)-a_(2)))^(2)`
where, `a_(1)` and `a_(2)` are the amplitudes of the waves take part in the superposition.
`((a_(1)+a_(2))/(a_(1)-a_(2)))^(2)=(16)/(1) rArr (a_(1)+a_(2))/(a_(1)-a_(2))=(4)/(1)`
`rArr a_(1)+a_(2)=4a_(1)-4a_(2) rArr 5a_(2)=3a_(1)`
`rArr (a_(1))/(a_(2))=(5)/(3) and (sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))-sqrt(I_(2)))=(4)/(1)`
`rArr sqrt(I_(1))+sqrt(I_(2))=4sqrt(I_(1))-4sqrt(I_(2)) rArr 5 sqrt(I_(2))=3sqrt(I_(1))`
`rArr (sqrt(I_(1)))/(sqrt(I_(2)))=(5)/(3) rArr (I_(1))/(I_(2))=(25)/(9)`