Tuesday, May 3, 2016

A Gentle Color Paradox

In my recent web-browsing, I ran across an exercise for students [1]: “If the wavelength of the green line of mercury is 546 nm in a vacuum, what is it in water? In heavy flint glass? [410 nm, 331 nm].”

This awakened me to a question I have not seen posed by color science. Would the color of a light change as drastically as suggested by the wavelengths in the above paragraph? [Strictly speaking, of course, the waves have no intrinsic color, but I use loose terminology for convenience, with the understanding that the only meaningful connection is a cetera paribus color match.]

The effect of wavelength shift would depend upon the context. Surely placing a piece of flint glass in air between a mercury-line lamp and a human viewer would not influence the wavelength of light arriving at the eye. Although the wavelength 546 nm would change to 331 nm while the light was within the glass, it would change right back to 546 nm as soon as it re-entered the air. Then it would change to its value of 410 nm upon entering the aqueous medium of the eye and photoreceptor system. (Of course, the light’s frequency would always be the same.) But we wouldn’t notice any change due to the 546-to-410 nm transition because we always see through the same aqueous medium (with the same refractive index) embedding the photoreceptors. 546 nm as measured by a spectroradiometer is hence calibrated to be identical to 410 nm as incident on our photoreceptors.

But suppose we change the refractive index of the material abutting the eye’s photoreceptors and see if the color of the refracted light changes. Even though abutting the photoreceptors with a non-waterlike substance seems impossible with real eyes, it is an option with cameras whose photosensors are embedded in the chosen refractory material; also, visual prostheses in the future could have this option. 

So, under these circumstances, would the color of a light change as drastically as suggested by the wavelengths recited in [1]? If the color did not change, then for this weird situation one should compute tristimulus values with frequency rather than wavelength as the integration variable: light does not change frequency when passing through a transparent medium. Perhaps someone has already tested the idea with cameras. I await the impact of the idea once prosthetic eyes are abundant.

[1]. HQ Fuller, RM. Fuller, and RG Fuller, Physics Including Human Applications. Harper and Row, 1978. Revised electronic version copyright 2009 by RG Fuller. http://physics.doane.edu/hpp/Resources/Fuller3/pdf/F3Chapter_19.pdf exercise 2, p. 436.

Michael H. Brill

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