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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.

A
The intensities of both the maxima and the minima increase
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B
The intensity of the maxima increases and the minima has zero intensity
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C
The intensity of the maxima decrease and that of the minima increases
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D
The intensity of the maxima decreases and the minima has zero intensity
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Solution

The correct option is A The intensities of both the maxima and the minima increase
The intensities due to slits are proportional to their width.
When we takes slits of equal width
I1I2=W1W2=1
I1I2=a2b2=1
or ab=1
ImaxImin=(a+b)2(ab)2=(ab+1)2(ab1)2=(1+1)2(11)2=20
This implies maximum intensity Imax is 2 and minimum intensity Imin is zero.
When we take the width of one slit is twice of the other
I1I2=W1W2=2
I1I2=a2b2=21
or ab=21
ImaxImin=(a+b)2(ab)2=(ab+1)2(ab1)2=(2+1)2(21)2.
This implies maximum intensity Imax is (2+1)2 and minimum intensity Imin is (21)2.
Therefore, the intensities of both the maxima and minima increase.

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