For a single slit of width 'a', the first minima of the interference pattern of a monochromatic source of light of wavelength lambda occurs at an angle of lambda/a. For the same angle of lambda/a, we get a maxima for two narrow slits separated by 'a'. How can this be explained?
The angle will be λ/a.
Here, the statement considers interference as a general term to represent both diffraction (and interference phenomenon in a single slit) and interference by two slits. In terms of a physical point of view, diffraction is also interference of secondary wavelets from a single slit.
From the theory of diffraction, we know that the minima condition is given by
nλ = a sinθ
For first minima n =1 =>λ = a sinθ
As because θ is small we have sinθ≈θ=>λ = aθ=>θ=λa
Thus in the single slit, the first minima occur at λ/a angle.
But when we consider the interference of two slits separated by a distance a and the distance of the screen from the slit is D, the position of the first maxima is given by
y=λDa
Again, y is small compared to D.
y=Dθ=>λDa=Dθ=>θ=λa
This means in the case of two slits we have a maximum at λ/a angle.
The angle will be λ/a.
Here, the statement considers interference as a general term to represent both diffraction (and interference phenomenon in a single slit) and interference by two slits. In terms of a physical point of view, diffraction is also interference of secondary wavelets from a single slit.
From the theory of diffraction, we know that the minima condition is given by
nλ = a sinθ
For first minima n =1 =>λ = a sinθ
As because θ is small we have sinθ≈θ=>λ = aθ=>θ=λa
Thus in the single slit, the first minima occur at λ/a angle.
But when we consider the interference of two slits separated by a distance a and the distance of the screen from the slit is D, the position of the first maxima is given by
y=λDa
Again, y is small compared to D.
y=Dθ=>λDa=Dθ=>θ=λa
This means in the case of two slits we have a maximum at λ/a angle.
