First slide

Coherent sources and their importance in interference

Question

In interference pattern, if the slit widths are in the ratio 1 : 9. Then find out the ratio of minimum and maximum intensity.

Moderate

A

1 : 2
B

1 : 4
C

2 : 1
D

4 : 1

Solution

Slit width ratio $\frac{ω_{1}}{ω_{2}} = \frac{1}{9} ∵ \frac{ω_{1}}{ω_{2}} = \frac{a_{1}^{2}}{a_{2}^{2}} = \frac{1}{9} \Rightarrow \frac{a_{1}}{a_{2}} = \frac{1}{3} \Rightarrow 3 a_{1} = a_{2} N o w, \frac{I_{\min}}{I_{\max}} = \frac{{(a_{1} - a_{2})}^{2}}{{(a_{1} + a_{2})}^{2}} = \frac{{(a_{1} - 3 a_{1})}^{2}}{{(a_{1} + 3 a_{1})}^{2}} = \frac{4}{16} = 1 : 4$

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