In a double slit experiment instead of taking slits of equal widths, one slit is made twice as wide as the other. Then, in the interference pattern [2000]

Question

In a double slit experiment instead of taking slits of equal widths, one slit is made twice as wide as the other. Then, in the interference pattern [2000]

Smart Achievers · Accepted Answer

(1)

When slits are of equal width,

$I_{\max} \propto {(a + a)}^{2} = (4 a^{2})$

$I_{\min} \propto {(a - a)}^{2} = (0)$

When one slit's width is twice that of the other,

$\frac{I_{1}}{I_{2}} = \frac{W_{1}}{W_{2}} = \frac{a^{2}}{b^{2}}$ $\Rightarrow \frac{W}{2 W} = \frac{a^{2}}{b^{2}}$ $\Rightarrow b = \sqrt{2} a$

$∴$ $I_{\max} \propto {(a + \sqrt{2} a)}^{2} = (5.8 a^{2})$

$I_{\min} \propto {(\sqrt{2} a - a)}^{2} = (0.17 a^{2})$

Clearly, the intensities of both the maxima and minima increase.

Solution

Q.
In a double slit experiment instead of taking slits of equal widths, one slit is made twice as wide as the other. Then, in the interference pattern [2000]

1 the intensities of both the maxima and the minima increase

2 the intensity of the maxima increases and the minima has zero intensity

3 the intensity of the maxima decreases and that of the minima increases

4 the intensity of the maxima decreases and the minima has zero intensity

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