An infinite metal sheet lies in the plane of the paper (z=0 in the drawing below, and has a pair of parallel slits cut i

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An infinite metal sheet lies in the plane of the paper (z=0 inthe drawing below, and has a pair of parallel slits cut into it.The surrounding medium is vacuum. The separation of the slits is w.Each slit has a width, a, and a height, b. These slits areilluminated by a monochromatic plane wave, E(x, y, 0, v),originating at a distance, z<<0 (behind the page ) and has anelectric field polarization in the x – direction only. The width ofthe slits, a and b, is on the order of the wavelength , λ. Find theintensity distribution, I(x, y, L, v), at a distance, z=+L. Pleaseassume that all distances, a, b, and w, along with the wavelength,λ, are much smaller than L. The Fraunhofer integral for E(x, y, z,v) below, which is valid in the far field, may be helpful. In thisformula, the constant k=2π/λ is the propagation vector magnitude,and the vector is pointed in the +z direction (out of the page).You wil recall that intensity, I, on a plane is the time averageover many wavelengths of the normal component of the Poyntingvector, S.
E(x, y, L, v) = (eikz /iλz) ei(k/2z)(x2+y2) ∫ⴄ=-ꚙ+ꚙ ∫ᶓ=-ꚙ +ꚙ E (ᶓ, ⴄ, 0, v)e-i2π (x/λz)ᶓ e-i2π(y/λz)ⴄ dᶓdⴄ
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