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(B) The ratio of slit widths is given by $\frac{w_1}{w_2} = \frac{1}{9}$.Since the intensity $I$ is proportional to the slit width $w$ and the square

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$4:1$

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(B) The ratio of slit widths is given by $\frac{w_1}{w_2} = \frac{1}{9}$.Since the intensity $I$ is proportional to the slit width $w$ and the square of the amplitude $a$,we have $\frac{I_1}{I_2} = \frac{w_1}{w_2} = \frac{a_1^2}{a_2^2} = \frac{1}{9}$.Taking the square root,we get $\frac{a_1}{a_2} = \frac{1}{3}$,which implies $a_2 = 3a_1$.The ratio of maximum intensity to minimum intensity is given by $\frac{I_{max}}{I_{min}} = \frac{(a_1 + a_2)^2}{(a_1 - a_2)^2}$.Substituting $a_2 = 3a_1$,we get $\frac{I_{max}}{I_{min}} = \frac{(a_1 + 3a_1)^2}{(a_1 - 3a_1)^2} = \frac{(4a_1)^2}{(-2a_1)^2} = \frac{16a_1^2}{4a_1^2} = \frac{4}{1}$.Thus,the ratio is $4:1$.

In an interference pattern,if the ratio of slit widths is $1:9$,find the ratio of maximum to minimum intensity.

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