what is the minimum width of a single slit that will produce a first minimum for a wavelength lamda
Answers
Explanation:
Width of the slit is a
The path difference between two secondary wavelets is given by,
Nλ=asinθ
Since, θ is very small, sinθ=θ
So, for the first order diffraction n=1, the angle is
a
λ
Now, we know that θ must be very small θ=0 (nearly) because of which the diffraction pattern is minimum.
Now for interference case, for two interfering waves of intensity l
1
and l
2
we must have two slits separated by a distance.
We have the resultant intensity, l=l
1
+l−2+2
l
1
l
2
cosθ
Since, θ=0 (nearly) corresponding to angle
a
λ
, so cosθ=1 (nearly)
So,
l=l
1
+l
2
+2
l
1
l
2
cosθ
l=l
1
+l
2
+2
l
1
l
2
cos0
l=l
1
+l
2
+2
l
1
l
2
We see the resultant intensity is sum of the two intensities, so there is a maxima corresponding to the angle
a
λ
.
This is why at the same angle
a
λ
we get a maximum for two narrow slits separated by a distance a.
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