The Fresnel integrals have the asymptotic forms (corresponding to large values of w) given by

Using this fact, show that the irradiance in the shadow of a semi-infinite opaque screen decreases in proportion to the inverse square of the distance to the edge, as z₁ and therefore v₁ become large.

w E(w) = ! +(-)sin W 2 W TTW y? cos S(w) = }