Can You Explain This Simple Lens Conundrum?

Simple positive lenses without color correction will focus blue light closer to the lens than red light because the index of refraction is higher in the blue than in the red. A reading magnifying glass which might typically have an 8 inch effective focal length, is such a lens. It was surprising to the author to observe, when looking at a colored map with such a magnifier, that the red markings appeared further away from the observer than the blue, green, and black markings.

We assume a lens of 8.000 inch focal length for red light for the lens which is held 4.000 inches from the map and viewed 8.000 inches from the lens. If one applies simple lens formulae or even exact ray tracing, one finds (as shown in the illustration, which is to scale) that the red image for 706.5 nm light with BK7 glass will be minus 8.000 inches from the lens and have a magnification of minus 2.000. When the same is done with the blue 404.7 nm light, the image is at minus 8.2801 inches and has a magnification of minus 2.070, as drawn.

This would at first seem to imply that red objects would appear closer when viewed simultaneously with both eyes, but they do not! Red objects appear to be further away from the observer than blue, green, and black markings. This is interpreted to mean that: what is observed is due to the magnification being greater for the blue than the red. Hence, objects that are magnified more are interpreted as being closer, and this seems to override the red image actually being closer to the observer, when interpreted by the mind.

If you have a different interpretation, the author would be pleased to receive it.

ron@willeyoptical.com

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