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?


The reason a wavelength change results in magnification can be understood from several different perspectives. An easy one is to consider a holographic lens: its focal length is strongly wavelength dependent. Another easy one is to do wavelength-dependent ray tracing through a simple hologram. A graphical method to do wavelength-dependent ray tracing is described in pseudocolor holography. Yet another way is to consider an ordinary glass lens, in which the refractive index varies with wavelength: because the refractive index varies with wavelength, the focal length varies with wavelength; and because magnification varies with focal length, magnification depends on wavelength even for a simple glass lens. It just depends a lot more strongly on wavelength in a holographic lens than in a glass lens.


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