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A transparent blue inkjet cartridge looks deep blue, a red one looks deep red, but a yellow one looks red. Tea also looks yellowish when it's shallow and reddish otherwise. Red is another colour, a different wavelength, so why does deep yellow look red?
Not all liquid or things that are yellow become red when they exist in large quantity. For example, beer, vegetable oil, and normal urine never look red even in large quantity, like in a vat. It really depends on the optical properties of the liquid and the suspended particles in it.
The optical properties of something depend on both its intrinsic factors such as its reflectance, transmittance, and absorptance of the light and the extrinsic factors such as its thickness, the surface that it’s on, the angle of light incidence, and the polarization of the incident light. (This is not to mention psychological factors like the mood when you look at that thing or the surroundings colors or compositions of that thing, which can make that thing look different.)
That’s why a thin film of water is colorless but a large body of water like the lake looks blue. And that’s why there is a phenomenon called iridescence – the phenomenon that certain surfaces appear to change color as the angle of view or the angle of illumination changes – like changing rainbow colors on a soap bubble or on a colorless CD surface.
In your case, I think the color reflection and transmission properties of the ink are different. The ink probably reflects mainly the yellow color, so it looks yellow when reflection of colors is the major event – as when the ink is painted on a surface. But the ink probably transmits more of the red color than the yellow color, so it looks red when transmission of colors is the major event – as when you look through it.
N.B. I think you’ll probably get better answers than mine by posting the question on the Physics forum.
References.
II.8. Reflection, Transmission, and Absorption Gigahertz-Optik.
Elements that Affect the Appearance of Color Konica Minolta.
Iridescence Wikipedia.
