Two slits in Young's experiment have widths in the ratio `1:25`. The ratio of intensity at the maxima and minima in the interference pattern `I_(max)/I_(min)` is

Options

A. `(49)/(121)`
B. `(4)/(9)`
C. `(9)/(4)`
D. `(121)/(49)`

Answer

C

Explanation

As, intensity I `prop` width of alit W Also, intensity I `prop` square of amplitude A
`:.(I_(1))/(I_(2))=(W_(1))/(W_(2))=(A_(1)^(2))/(A_(2)^(2))`
But `(W_(1))/(W_(2))=(1)/(25)` (given)
`:.(A_(1)^(2))/(A_(2)^(2))=(1)/(25)"or"(A_(1))/(A_(2))=sqrt((1)/(25))=(1)/(5)`
`:.(I_("max"))/(I_("min"))=((A_(1)+A_(2))^(2))/((A_(1)-A_(2))^(2))=((A_(1))/(A_(2))+1)^(2)/(((A_(1))/A_(2)-1)^(2))`
`=((1)/(5)+1)^(2)/(((1)/(5)-1)^(2))=(((6)/(5))^(2))/((-(4)/(5))^(2))=(36)/(16)=(9)/(4)`