For the fold caustic discussed in the text, assume that the phase change introduced by the imperfect lens is nondispersive, so that the (a, x)

For the fold caustic discussed in the text, assume that the phase change introduced by the imperfect lens is nondispersive, so that the φ(ã, x̃) in Eq. (8.45) satisfies φ ∝ λ⁻¹. Show that the peak magnification of the interference fringes at the caustic scales with wavelength, ∝ λ^−4/3. Also show that the spacing △x of the fringes near a fixed observing position x is ∝ λ^2/3. Discuss qualitatively how the fringes will be affected if the source has a finite size.

(x) x dei(,x) xf de = f =f da d (cos o + i sin o), where = 3 x. (8.45)