# Temporal Colour Mixing

#### Abstract

A square wave signal applied to a bi-directional LED demonstrates temporal mixing of colours: a light that flashes red-green-red-green rapidly will appear yellow.

Yes

#### Principles Illustrated

We use a bi-directional LED that produces red light when a current flows in one direction and green light when a current flows in the other direction. When a square wave is applied the LED flashes red and green. As the frequency is increased the individual flashes are no longer visible and the LED appears yellow. A high speed video camera reveals that the LED is still alternating red and green even when the bulb appears yellow.

As discussed in Computer Colours, a computer screen ‘fakes’ yellow and other colours using red, green, and blue lights that are very close to each other. With the red and green lights within a pixel lit up, one sees yellow. This is spatial colour mixing.

One can also mix colours temporally, time-wise. If red and green lights in the same place are flashed separately – never both on at once – what will you see? If the green and red flashes last a second each you will of course see them separately and clearly. But as the frequency increases to 20 flashes per second or so, the green and red flashes start to meld into yellow. At 50 Hz you cannot see that there are flashes at all. You just see a yellow light. But the high speed camera shows that the LED is still flashing red and green. See video clips below.

Of course if the LED flashes fast enough even the high speed camera cannot see the individual flashes and the LED appears yellow. The high speed camera takes 1000 frames per second. If the signal generator frequency is at or above half of this rate (500 Hz or more) the camera will fail to catch all of the red and green flashes (this is essentially Nyquist’s theorem). A short video clip below was taken with the LED flashing at more than 22 kHz, far too fast for the camera to catch the individual flashes.

Note that movies and videos on computer screens run at about 24 frames per second (there is some variation).. This is fast enough that you cannot see clearly the individual frames and the video appears more or less continuous. Some early web cams operated at slower frame rates and the motion did not appear to be continuous.

Jnr Sci

#### Instructions

Bi-colour LEDs are readily available in New Zealand at very low cost from Jaycar, Element 14, and other electronic component suppliers. We paid \$1.50 for ours. The bi-colour LED bulb actually contains two LEDs arranged as indicated in the diagram below. When a voltage is applied with one polarity the green LED lights up and when the voltage is applied with the other polarity the red LED lights up. You cannot light up both LEDs at the same time with this type of bi-colour LED.

You will need a signal generator (function generator) capable of producing a bi-polar square wave such as the one sketched below with an amplitude of a few volts. A positive square wave (on-off-on-off) will not work. Signal generators are expensive but most schools will have a suitable one in the physics lab. It is possible to use the speaker output of a computer as a signal generator, but this requires some software.

You will need a current-limiting resistor in the circuit, and the specifications for the diode will sometimes recommend a value for the resistor. If not, you can calculate an approximate value by dividing the maximum voltage you intend to apply (usually the amplitude of your square wave) by the current limit for the LED. This calculation ignores the voltage drop across the diode itself, but it is close enough and overestimates the resistance you need, thus making a blown diode less likely.

#### Safety

Individual teachers are responsible for safety in their own classes. Even familiar demonstrations should be practised and safety-checked by individual teachers before they are used in a classroom.