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.

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(x) x dãei(ā,x) xf dãe¹ = f =f da dã (cos o + i sin o), where = ã³ 3 xă. (8.45)