LESSON

Light and blackbody light sources

Transcript

The first stage in the process is the illuminant; that is, what creates the light that falls on the scene that is ultimately reflected into our eyes. So where does the light come from? Well there are many, many different sources of light; incandescence’s is emitted by hot objects, that could be the white hot filament of a tungsten light bulb or it could be the sun.

Old fashion cathode ray tubes—as found in televisions and old computer monitors—generate light by firing very energetic electrons at phosphors and these are chemicals that accept that high energy electron and convert that into photons or light.

We also have light emitting diodes, gas discharge tubes and lasers.

Way back in 1672, Isaac Newton developed what he called the spectral theory of light and he did a very famous experiment, light entered the room through a hole in a covering over the window and entered a prism where he saw that it was split into many different colors.

And then he was able to show that he could recombine the multiple colors of light back into a single beam of white light.

What you see here is an image of Isaac Newton’s notebook that records this experiment that he did.

A very iconic image is of a beam of white light entering a prism and being split into all of the colors of the rainbow. These different colors represent light of different frequencies and we tend to describe the frequency of a particular color of light in terms of its wavelength. It is a length and it is measured in units of nanometers; ten to the minus nine meters. Now, not all light is visible, human beings are able to see light between about 400 nanometers and 700 nanometers. Light with wavelengths shorter than 400 nanometers we refer to as ultra-violet and light with wavelengths greater than 700 nanometers we refer to as infra-red.

Light is an electromagnetic wave and if we look at this graphically we see that there are two
self-reinforcing waves, moving through space in this direction along the x axis. One of those waves is an electric field; the other wave is a magnetic field. The length of a single cycle of either of these waves we refer to as the wavelength and very commonly give it the symbol lambda.

So the wavelength is the length of a single cycle of this electromagnetic wave and for light it is between 400 and 700 nanometers.

Let’s now consider black body radiators and the two most common black body sources of light that we use are the traditional incandescent tungsten light bulb, though these are now going out of fashion, and the sun. The sun is a very hot object in the sky that emits visible light.

The amount of light that a black body radiator emits as a function of its wavelength is given by this curve here. The visible range of light is shown here. This curve is described by Planck’s law and it contains a large number of constance, and one of the terms in this expression is T, that is the temperature of the black body radiator. That is the temperature of the tungsten filament or it is the temperature of the surface of the sun.

Typically, these are in the order of thousands of degrees Kelvin. The curve has got a very clear peak, and the wavelength of this peak is given by the Wien displacement law, and what this shows is that the wavelength associated with the maximum of this peak is inversely related to the temperature.

So low temperatures have a large lambda associated with the peak and as the temperature increases this lambda acts, decreases. It moves to a shorter wavelength. And we actually have an intuitive feel for this: what I have plotted here are the black body emission curves for black bodies at a range of different temperatures—from 1000 Kelvin up to 6000 Kelvin—and as we can see, as the temperature increases, the wavelength associated with the maximum is moving towards a smaller wavelength … it is becoming more blue. So as its temperature increases, the wavelength associated with the maximum emission moves to lower wavelengths, to bluer colors.

In our language we use colors to describe temperatures. Something that is pretty hot, metal that is just about to begin be able to be worked, we describe as being red hot. As we increase the temperature it becomes yellow hot, it is glowing a different color, it is more yellow now and as the temperature goes up it starts to omit white light. And we refer to that as being white hot.
Let’s have a go at plotting one of these black body curves. To get started with, just to make life a little bit easier for myself I am going to define a symbol NM, stands for nanometer and is equal to one by ten to the minus nine. Make life a little bit easier.

And I am going to create a vector of wavelengths. I am going to call it lambda and it is going to vary from three hundred nanometers in steps of ten nanometers all the way up to a thousand nanometers, this is going from the near ultra-violet through into the infra-red part of the spectrum.

Now I can compute a black body radiator emission curve, using the black body function. I pass in the range of wavelengths that I am interested in and I pass in the temperature. And I am going to put in 6500 Kelvin, which is the temperature of the sun. I can plot this curve, one axis is going to be lambda and the other axis is going to be E. And here we have a plot of the response of the black body radiator. I am going to put a grid on there.

Let’s look at the case now for a black body radiator, but at a lower color temperature and I am going to reduce the color temperature a little bit.

So let’s come back here and I am going to reduce the color by 500 degrees. Put that into the variable E. I am going to overlay that plot and now I am going to plot E against lambda and I am going to do it with dashline so we can see what’s the difference. And what we can see is that the curve is lower; this slightly cooler body is emitting less energy overall. The peak of its omission has moved from around 450 nanometers to closer to 480 nanometers. So it has got a little bit cooler and it is a little bit more red in its appearance.

The light we see is a mixture of different wavelengths in the visible region of the electromagnetic spectrum. The most common source of light is incandesence from a very hot body such as our sun or the filament of an old-fashioned light bulb. The spectrum, the amount of energy as a function wavelength, follows Planck’s law for a black body radiator and varies with temperature.

Professor Peter Corke

Professor of Robotic Vision at QUT and Director of the Australian Centre for Robotic Vision (ACRV). Peter is also a Fellow of the IEEE, a senior Fellow of the Higher Education Academy, and on the editorial board of several robotics research journals.

Skill level

This content assumes an understanding of high school-level mathematics, e.g. trigonometry, algebra, calculus, physics (optics) and some knowledge/experience of programming (any language).

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