A light wave of wavelength & travels from A to B by passing through an aperture (circular region) located in a plane that is perpendicular to AB (see Figure 11 for the notation). Let /() = d' + ': that is, f() is the distance AC + CB as a function of r. (a) Show that /(r) = vd- tri + v/? + , and use the Maclaurin polynomial of order 2 to show that (b) The Fresnel zones, used to determine the optical disturbance at B, are the concentric bands bounded by the circles of radius R. such that (R.) = d + h + nx/2. Show that R,, can be approximated by R. " VALL, where I = ( + . (c) Estimate the radii R, and Rion for blue light () = 475 x 10-7 cm) if d = h = 100 cm. o B FIGURE 11 The Fresnel zones are the regions between the circles of radius Rn