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A real-time view of a similar visual effect...
The images below are photographs taken of my [Peter's] desk, lit solely by the desk lamp, fitted with a 60 Watt tungsten bulb. (They may take a little time to load...)

The first shows the pattern of illumination exactly as recorded by the camera. (Strictly speaking, I had to set the camera to a daylight white balance; in automatic mode it did a fair job of compensating for the skewed light levels.)

Tungsten illumination of Peter's desk

The overall cast is orange, but notice that the computer screen looks to have reasonably realistic colours: in particular the greys of the Photoshop backgrounds have been faithfully recorded. This is because I have my monitor set to a colour temperature of 6500 K (which approximates the frequency distribution on a bright sunny day), while a tungsten filament has a much yellower colour temperature of about 3400 K. The result is that the monitor exposes correctly, while the rest of the room is orange.

The image below was adjusted in Photoshop to correspond as broadly as possible with my own idea of the colours in the scene, with the exception of the monitor (qv below).  The desk and plastic mouldings are now the correct colour (I used the drawing tablet surface at bottom right to set the grey point for the image), and the cup and pens have the correct hue.

'Daylight' illumination of Peter's desk

There's an interesting point here. The second view is artificially altered to make the background appear 'correct', but doing so causes the monitor screen to be too blue. (This effect would also have been achieved if I had set my digital camera to a 'tungsten' setting, or used indoor film in a standard SLR.)

But, looking at the scene 'live' (as I'm typing these words), I see both the screen and the surroundings as being correct – something like a combination of the screen from the first image and the background from the second. Even flicking my eyes from screen to background and back again, my visual system is compensating in real time, without any problem.

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