Dear Tristan,

the edge of the ruler acts as a prism. A prism displaces the view according to color. You can imagine the view of the white (W) sheet as a superposition of red (R), green (G) and blue (B) views, W = R + G + B, according to the laws of additive RGB color mixing.

Through the prism, the blue view is always shifted the most (with respect to the direct view without a prism), whereas the red view is always shifted the least.

The views are always shifted toward the edge of the prism.

If the edge is pointing upward, the blue view is shifted upward more than the red, so you see a cyan (G + B) and blue (B) fringe above the otherwise white (R + G + B) sheet.

If the edge is pointing downward, the blue view is shifted downward more than the red, in other words: the red view is shifted downward less than the blue, so you see a yellow (R + G) and red (R) fringe above the otherwise white (R + G + B) sheet.

The color effect only occurs at the borders because there, some of the colored views are absent (shifted downward or upward). At other places, there is a complete superposition of R, G and B. You can simulate this by illuminating a white wall with red, green and blue rectangles, and mutually shifting the rectangles by a small amount.

You observe the same effect with the blue ruler because you can still see red and green objects through it, just fainter. With a perfectly blue ruler (through which red and green objects appear black), there would be no color fringes.

See my article "An RGB approach to prismatic colours".

As a general rule, the absolute width of the fringe (as measured where the object appears to be) is proportional to the distance between the prism and the object, and independent of the distance between the viewer and the prism.

This general rule has two specific consequences.

First: For a camera directly at the prism, the shift takes up the same number of photo pixels for any object distance. So foreground objects will have the same (angular) width of color fringes as background objects. So, yes, the effect applies to all object distances.

Second: For a camera at some distance from the prism, the fringes of foreground objects take up fewer photo pixels than the fringes of background objects. So, yes, indeed, you can infer 3D geometry from such photographs, simply based on the width of the color fringes.

You may find José Lunazzi's work interesting.

Kind regards,

Sascha Grusche

It is some form of chromatic aberration. Polystyrene and many plastics like acrylics and polycarbonates have low Abbe numbers, in the 30s, which indicates they are highly dispersive. Dispersion is a consequence of the index of refraction being dependent on wavelength. Unless the window is of uniform thickness and parallel, it will act as a lens or a prism and the color shift / focus shift will be evident.

Hi Tristan,

As suggested by Robert the observed colour bands are formed when an ambient light beam has been separated out into a divergent set of component beams, each with a distinct spectral colour.

Consider if you will Isaac Newton’s classic experiment where he revealed the colours of the spectrum by passing a narrow beam of white light through a prism. On passing through each surface of the prism each of its component colours is seen to be bent onto a distinct wavelength-dependent path.

The observed change of direction is caused by a change in the speed at which the light is propagated through the solid prism as compared with that in air. As an aside, the conventionally unattainable ‘speed of light’ is that of electromagnetic radiation in a perfect vacuum.

Returning now to the rulers, the necessary prism-like angles must clearly be present at the edges of each ruler and they will necessarily disperse the ambient light like a rather rough and uneven prism. Putting two or more such objects close together may then either reverse or enhance the overall light bending effect.

The change from orange to blue according to orientation is simply a matter spectral-sampling as a function of viewing angle. The fact that the blue ruler has the same effect as the white one is direct confirmation that the observed phenomena are caused by the polystyrene not its apparent colour.

Dear Tristan,

the edge of the ruler acts as a prism. A prism displaces the view according to color. You can imagine the view of the white (W) sheet as a superposition of red (R), green (G) and blue (B) views, W = R + G + B, according to the laws of additive RGB color mixing.

Through the prism, the blue view is always shifted the most (with respect to the direct view without a prism), whereas the red view is always shifted the least.

The views are always shifted toward the edge of the prism.

If the edge is pointing upward, the blue view is shifted upward more than the red, so you see a cyan (G + B) and blue (B) fringe above the otherwise white (R + G + B) sheet.

If the edge is pointing downward, the blue view is shifted downward more than the red, in other words: the red view is shifted downward less than the blue, so you see a yellow (R + G) and red (R) fringe above the otherwise white (R + G + B) sheet.

The color effect only occurs at the borders because there, some of the colored views are absent (shifted downward or upward). At other places, there is a complete superposition of R, G and B. You can simulate this by illuminating a white wall with red, green and blue rectangles, and mutually shifting the rectangles by a small amount.

You observe the same effect with the blue ruler because you can still see red and green objects through it, just fainter. With a perfectly blue ruler (through which red and green objects appear black), there would be no color fringes.

See my article "An RGB approach to prismatic colours".

As a general rule, the absolute width of the fringe (as measured where the object appears to be) is proportional to the distance between the prism and the object, and independent of the distance between the viewer and the prism.

This general rule has two specific consequences.

First: For a camera directly at the prism, the shift takes up the same number of photo pixels for any object distance. So foreground objects will have the same (angular) width of color fringes as background objects. So, yes, the effect applies to all object distances.

Second: For a camera at some distance from the prism, the fringes of foreground objects take up fewer photo pixels than the fringes of background objects. So, yes, indeed, you can infer 3D geometry from such photographs, simply based on the width of the color fringes.

You may find José Lunazzi's work interesting.

Kind regards,

Sascha Grusche