Magnification in Holographic Microscopy

The book "Introduction to Optics" by Frank, Leno, and Leno Pedrotti, Ed 3, makes the claim that

It can be shown that if the reconstructing light of wavelength $\lambda_r$ is longer than the wavelength $\lambda_s$ used in "holographing" the subject, a magnification given by $$M = \frac{q}{p}\frac{\lambda_r}{\lambda_s}$$ results, where p is the object distance (subject from film) and q is the corresponding image distance (image from hologram).

However, the book does not show why this is the case and my attempts to find the reason online have not yet been successful.

Why does reconstructing light with a longer wavelength than that used to record the interference pattern on the hologram result in magnification?