If the two slits in Young's experiment have width ratio `1 : 4`, deduce the ratio of intensity at maxima and minima in the intereference pattern.

Options

A. `9:1`
B. `3:1`
C. `9:2`
D. `10:3`

Answer

A

Explanation

Intensity `prop` width of slits width `prop ("amplitude")^(2)`
`I prop ("Amplitude")^(2)`
`therefore (I_(1))/(I_(2)) = (a^(2))/(b^(2)) = (1)/(4) rArr (1)/(2) = (a)/(b)`
So, width `prop` intensity
or b = 2a
`therefore (I_("max"))/(I_("min")) = ((a+b)^(2))/((a-b)^(2)) = ((a+2a)/(a-2a))^(2)`
`((3a)/(-a))^(2) = (9)/(1)`
`therefore (I_("max"))/(I_("min")) = (9)/(1)`