The Human Eye
The last part of the process is what goes on in the eyes of the observer. We refer to this as the response and like everything else the response is a function of the wavelength lambda. In fact the response can be written this way: it is the integral over wavelengths of the spectrum of the incoming light of the reflectance and of the response of the eye to light at that particular wavelength. So what we sense in the photoreceptor cells in the back of our eye is essentially the result of this particular integral. Let’s see how that works.
Here is a cut away diagram of the human eye; at the back of the eye we have the retina and we are looking at the surface of the retina; we see a lot of blood vessels and we can see the optic nerve, which is what connects the eye to our brain. If we take a cross section through the retina, make a slice through there, we look downwards. We see that there are layers of nerves and other sorts of cells. And at the bottom of this stack we have the light sensitive cells and they look something like this.
So what is quite surprising is that the light sensitive cells are not on the surface of the retina. They are actually about 500 micrometers below the surface of the retina. So the light that falls on the retina has to fight its way down through blood vessels and nerve cells and all sorts of things to get to the light sensitive rod and cone cells.
Let’s look at the rod cells. They’re these small worm-shaped objects that we see in the back of the retina. They contain a chemical called rhodopsin. And it is a quite important chemical, because when a photon of light hits it, it changes its shape, and changes its shape from this, to that. And we can see that one arm of the molecule is in fact being spun around by the impact of the photon and that is eventually converted into an electrical signal, which travels along the optical nerve to the visual cortex of your brain. The rod cells are very sensitive to light, so these are the cells we use in low light conditions. This is what we use at night, and the way they are wired makes them also very sensitive to motion and it is what we use to determine that something is moving in the edge of our field of view.
The rod cells are sensitive to a range of electromagnetic radiation as shown by this graph here. So this is the response curve of the rod cells and we denote it by the symbol M and it, of course, is a function of wavelength lambda. The rod cells are maximally responsive to light at 498 nanometers. Basically, mid green color.
The other very important class of cells in the human eye are the cone cells, and one of them is indicated here. They are not that conical. They are certainly fatter at the bottom then they are at the top. Quite a different shape to the rod cells. The cone cells contain chemicals called photopsins; they are related to rhodopsin that we have in the rod cells. There are different flavours of photopsins that are sensitive to light at different colors. The cone cells are what we use for our everyday daytime activities and in the daytime we use our cone cells, not the rod cells.
The cone cells contain a chemical called photopsin and photopsin is related to rhodopsin, but there are three different flavours of the photopsins, there are photopsins that are sensitive to red, to green and to blue light and so there are three different types of cones, those that are, that contain these different types of photopsin, sensitive to red, green and blue.
So we say that human beings are trichromats. It means that we have got cells that can sense three different colors, sensitive to different bands within the spectrum and that is what is shown in the graph over here. Often these bands are referred to by the letters S, M and L, which stand for short wavelength, medium wavelength and long wavelength. We would also refer them as blue, green and red … in that order.
The response of the short, medium and long cone cells are shown here. We can see that there is quite some overlap, particularly between the medium and long wavelength cone cells, and also shown here for reference is the response of the rod cells we looked at in the previous slide.
Let’s look more closely at the retina and there are two key landmarks in the retina. One is what we call the fovea, where we have an enormous concentration of light sensitive cells. The other big landmark which is where the optic nerve joins the retina, and that area has almost no light sensitive cells—it is actually a blind spot in your eye. So if we project those two points down and we draw an axis, we can plot the concentration, the density of cone cells as a function of angle away from the fovea. So on one side we have the direction towards your ear, on the other side we have the direction towards your nose and we can see there is an enormous concentration of cones in the fovea area and a much lower concentration of cone cells in the rest of your eye in what we call the peripheral vision area.
If we look now at the distribution of rod cells we see almost the converse; we see that there are very many rod cells in the peripheral parts of your vision, not too many of them at all in your fovea.
So the fovea, we have a very high concentration of color sensitive cells, the rest of the eye there are a large number of cells that are sensitive to light but don’t distinguish between different colors.
Light entering our eyes stimulates the photoreceptor cells in the retina of our eye: color sensitive cone cells that we use in normal lighting conditions and monochromatic rod cells we use in low light. The density of these cells varies across the retina, it is high in the fovea, low in the peripheral vision region and zero in our blind spot.
High school mathematics
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