First slide

Coherent sources and their importance in interference

Question

In Young's double slit experiment, if the slit widths are in the ratio 1 : 9, then the ratio of the intensity at minima to that at maxima will be

Easy

A

1
B

$\frac{1}{9}$
C

$\frac{1}{4}$
D

$\frac{1}{3}$

Solution

$Slit width ratio = 1 : 9 Since slit width ratio is the ratio of intensity and intensity \propto {(amplitude)}^{2} ∴ I_{1} : I_{2} = 1 : 9 \Rightarrow a_{1}^{2} : a_{2}^{2} = 1 : 9 \Rightarrow a_{1} : a_{2} = 1 : 3 I_{max} = {(a_{1} + a_{2})}^{2}, I_{min} = {(a_{1} - a_{2})}^{2} \Rightarrow \frac{I_{min}}{I_{max}} = \frac{1}{4}$

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