Seeing the Light Syllabus
This course covers many introductory features of light and vision. It concentrates on basic optics, images, optical instruments, anatomy of the human eye, photography, visual perception, wave phenomena, color and holography. In pursuing these topics, we attempt to develop the student's curiosity and powers of observation about the physical world. Understanding of these many topics is achieved through a healthy application of the scientific method and some exercise in using scientific models.
Reading: STL Chapter 2 -- sections 2.1-2.2, 2.4-2.6, Appendix B
Section 2.2 gives us the basics on shadows and the camera obscura. We will skip over section 2.3 on reflection of light waves until much later in the course. Section 2.4 introduces the all-important law of reflection and talks about diffuse versus specular reflection, retroreflectors and examples of natural reflection (glitter paths, sub suns and sun pillars). Section 2.5 introduces Snell's law of refraction (see also appendix B), the index of refraction, total internal reflection and fiber optics, and mirages. Section 2.6 talks about dispersion, which explains the colors of rainbows and diamonds.
Optional Reading: "Rainbows, Halos, and Glories" by Robert Greenler, on reserve in the Physical Science Library.
Chapter 1 discusses the details of rainbow formation and chapter 7 talks about mirages and the green flash. Several of the slides we show in class are taken from this book.
Many characteristics of light can be most easily understood in terms of the fact that light appears to move in straight lines. We will develop the notion of a light ray (which moves in straight lines) in order to understand many features of basic optics such as reflection and refraction.
(Later in the course we will find that there are some phenomena, such as interference and diffraction, that cannot be described by a model of light rays and it will be necessary to develop a wave model of light. Until then, the simple idea of light rays will describe most of what we want.)
Shadows from an extended light source, such as the sun, are comprised of two parts: the umbra (the darkest part), and the penumbra (the lighter edge of the shadow). We will look at the geometry of shadows that leads to this and study the behavior of eclipses.
A camera obscura uses a mask with a pinhole opening to project an image onto a screen or onto photographic film. The camera obscura is often used to look at the image of a solar eclipse without staring directly at the sun. For a tiny pinhole, the image is always in focus, independent of the distance to the object or the distance between the pinhole and the screen. As the pinhole is enlarged, the image becomes brighter and fuzzier, until for very large holes, the light on the screen shows only the shape of the hole.
The most fundamental principle at work here is the law of reflection: the angle a reflected light ray makes with the reflecting surface is the same as the angle of the incident light ray. This law works for reflection off of mirrors and we use it to understand the behavior of many types of mirrors. Later in the course, we try to understand the origin of this law in terms of Fermat's principle of least time.
The term "specular reflection" refers to reflection off of a smooth surface (from the latin "speculum" for mirror). For this type of reflection the law of reflection applies. We identify some features of images in mirrors (e.g. that they reverse left and right -- but why not top and bottom?) and note that curved mirrors can be understood as a combination of small planar mirrors. We learn how to count the number of images in sets of multiple mirrors and how a corner cube behaves as a retroreflector. (Retroreflectors are commonly used in bike reflectors and a retroreflector was put on the moon by Apollo astronauts in order to reflect laser beams from the earth.)
Diffuse reflection refers to reflection off of a rough surface, such as paper. Our primary examples of light reflecting off of wet and dry roads will clarify the difference between diffuse and specular reflection. We will note that at more grazing angles the reflected light is brighter and more like specular reflection.
As a light ray passes into a transparent medium, it changes direction. It also changes speed. These two facts are intimately related, as we shall see.
Very fast, but finite. Think about how fast lightning travels compared to thunder. The first reasonably accurate determination of the speed of light was made by Olaus Roemer in the 17th century by observing motions of the moons of Jupiter. We pause to appreciate how long it took for light to reach us from the most distant galaxies seen by the Hubble Space Telescope.
The index of refraction of a transparent material describes the ratio of the speed of light in that material compared to the speed of light in vacuum. It is also a key ingredient in determining how light bends as it moves from one medium to another (see Snell's law below).
As light travels from a medium with a lower index of refraction into a medium with a higher index of refraction, it bends towards the normal to the surface. The amount it bends is determined by the ratio of the two indices of refraction and the sine of the incident angle, and is known as Snell's law. We will examine an important application of this law in the refraction of light through a beer mug.
Fermat proposed that the path light travels is the path that takes the least time. Today we understand this principle as natural result of a quantum field theory of electromagnetism. In class, we will use the principle to demonstrate both the law of reflection and Snell's law of refraction.
Total internal reflection can occur as light travels from a medium with a high index of refraction towards a medium with lower index of refraction. If the approach to the interface is at a grazing angle, there will be no light transmitted to the lower index medium; all the light will be reflected. Such mirrors are therefore much better than conventional metallized mirrors, which usually reflect only 95 to 99% of the incident light.
Total internal reflection is used to great advantage in fiber optics. Once light is sent into a fiber optic, it can be made to reflect off the sides of the fiber at angles that are subject to total internal reflection. In this way the light will remain trapped inside the fiber and can be transported over large distances.
Dispersion refers to the fact that different colors of light travel at slightly different speeds in transparent media, and therefore refract at slightly different angles. This is the operating principle behind a prism.
We explore a number of natural phenomena that demonstrate reflection, refraction and dispersion.
Astronomers struggle with this all the time. As you look up through the atmosphere towards a star, the atmosphere disperses the starlight so that you may see a series of different colored images, as if you were looking through a prism. Fortunately, dispersion by the atmosphere is a small effect and is only noticable through a telescope. We will look at some photos of Venus at the horizon, which will show some striking effects of dispersion.
Why do you think? The atmosphere preferencially reflects blue light. This also explains why sunsets are red, and why distant hills sometimes look blue.
A very rare phenomena visible at sunset; it is the result of dispersion and scattering of sunlight by the atmosphere. I have yet to observe this myself.
Rainbows are the result of sunlight refracting and reflecting through water droplets in the sky. Dispersion in the droplets separates out the colors we see in the rainbow. We will spend most of one class period understanding the geometry of the rainbow, including some less common features such as double rainbows and reflected bows.
The romantically beautiful shining path of moonlight reflecting off of water is called a glitter path. A similar effect occurs from sunlight reflecting off of ice crystals in the sky, producing a sun pillar.
Halos around the sun or the moon are sometimes seen in the winter months. These magnificent effects are the result of light refracting through hexagonal ice crystals in the sky.
The density and index of refraction of air changes as the temperature changes. This fact can be used to explain how light refracting near the surface of the earth on a hot day may produce a mirage. A related effect, called a Fata Morgana mirage may occur on a cold day and can allow an earthbound observer to see well beyond the normal horizon.
This section on images introduces some of the rules of basic optics for mirrors and lenses. Herein we learn how to locate images in simple mirrors and lenses, and develop the useful tools of ray tracing and the lens and mirror equations. Mastering these simple rules will allow us to understand more complex instruments such as telescopes and microscopes in the next section.
We start by noting that there are two types of images. In the case of "virtual" images, such as the images produced by plane mirrors, light does not travel directly from the image to the eye. Light only appears to come from the image, which is located on the far side of the mirror. For "real" images, the light rays do originate at the image. An image projected on a screen is such an example. Light travels directly from the screen to the eye.
Reading: STL Chapter 3 -- sections 3.1-3.4
Section 3.2 introduces the idea of an image and teaches us how to locate images in single and multiple planar mirrors. Section 3.3 extends the discussion to images in spherical mirrors and explains the principles of ray tracing. Section 3.4 discusses image location and ray tracing in simple lenses, as well as Fresnel lenses (3.4D) and compound lenses (3.4E).
Here we use our knowledge of the law of reflection in order to calculate the location, orientation, size and type (real or virtual) of images produced by mirrors.
Plane mirrors provide the easiest example of images. We will apply the law of reflection to several light rays in order to determine that the image in a plane mirror is as far behind the mirror as the object is in front.
Have you ever noticed that images in a convex mirror always appear to be farther away than they would in a planar mirror? Look at the back of a shiny spoon or in the passenger side mirror of a car to see an example. Using the idea that curved mirrors can be thought of as a collection of tiny plane mirrors, we will calculate the location of images in a convex mirror.
Parallel light rays that are close to the axis of a spherical mirror will be reflected so that they appear to come from a single point in space. This convenient feature of spherical mirrors allows us to introduce the notion of focal point and focal length.
Knowing the path of only two light rays permits us to determine the image location of a point object. Conveniently, there are three types of rays that a particularly easy to identify, which will help us locate images. These are a) paraxial rays, b) rays headed for the center of the mirror and c) rays headed for the focal point of the mirror. These simple rays permit us to quickly identify the images in any convex mirror. Similar rules will be used to identify images in concave mirrors and thin spherical lenses.
The images in concave mirrors are a bit more interesting than in convex mirrors. Depending on how close the object is to the mirror, the image can be magnified or demagnified, real or virtual, upright or inverted. Very realistic images can be produced from the real images of concave mirrors. In class we will examine the puzzling case of the floating pig. Good examples of concave mirrors can be found in shaving mirrors, makeup mirrors and telescope mirrors. The ray tracing rules we learned previously will once again help us figure out each case.
How can you get two light rays to converge towards each other using a piece of glass. The answer is a lens. We will see that convex spherical lenses can cause light rays to converge while concave lenses cause light rays to diverge.
As in the case for spherical mirrors, it makes sense to define a focal point and a focal length for a lens. For additional convenience, we define the "power" of a lens, measured in diopters, to the be inverse of the focal length measured in meters.
A review of the pinhole camera, this time with a lens and many pinholes, shows us how a lens causes many pinhole images to overlap, creating a bright image on the screen.
Augustin Fresnel, in the early 19th century, devised a very clever way of removing most of the glass from a spherical lens while retaining all of the focussing ability of the lens. This allowed the construction of very flat, very light lenses. We will examine one terrific example in class.
Ray tracing in lenses works much the same way it did in mirrors. There are three rays that are particularly easy to trace in lenses. These three rays help us to locate the images quickly.
A spherical lens provides an interesting special case. A glass lens in air focuses light approximately at the back of the lens. If the lens is backed by a reflective surface (e.g. white paint) then light is reflected back the same direction it came from. This principle is used to manufacture reflective roadsigns by embedding small glass spheres in reflective paint.
Everything we learn from ray tracing can be embodied in a pair of simple equations (one for lenses and one for mirrors). The lens equation (and separately the mirror equation) relates the image location to the focal length of the lens and the object location, making it easier and faster to locate the image in simple optical systems.
As an application of the lens equation we will calculate the image location from a pair of lenses. This will relate to a number of optical instruments we will study next.
Using our knowledge of lenses and mirrors we can now understand the construction of more complex optical systems.
Reading: STL Chapter 6 -- sections 6.1-6.4, 6.6
Section 6.2 teaches us about some simple single-lens instruments such as reading glasses and magnifying glasses. Sections 6.3 and 6.4 describe two very similar instruments: the microscope and the telescope. Section 6.6 talks about field of view and field lenses, and how these relate to projectors and periscopes.
The simplest example. Learn how to prescribe reading glasses for your grandparents.
How do you get the largest magnification out of a lens? Learn why Sherlock Holmes always went around with a magnifying glass pressed to his nose. In some instances a magnifying glass can be used to reverse perspective, making more distant objects look bigger.
One could make a microscope out of a really strong lens, but the lens would have to be very small and it would be hard to look through. The easy way to make a microscope is with two lenses, the first lens (the "objective") creates a large intermedieate image of the object, the second lens (the "eyepiece") magnifies the intermediate image just the way a single magnifier does.
The original telescope designed by Galileo used a convex objective lens and a concave eyepiece. Modern astronomical telescopes use two convex lenses, inverting the image. Fortunately, stars look more or less the same whichever side is up.
The largest telescopes are made of mirrors rather than lenses. We will look at a number of popular designs for large telescopes, as well as some of the amazing images they bring us.
Radio telescopes operate off of the same principles as optical telescopes. Radio waves are just another form of light not visible to the human eye. The largest telescope is a radio telescope in Puerto Rico, the size of eighteen football fields.
Binoculars work much like a pair of telescopes set side by side. The one complication is a set of prisms that are used to turn the image right-side up.
The challenge for a slide projector is to achieve uniform illumination of the slide and to direct as much light as possible onto the focussing lens. In the slide projector this is accomplished with an ingenious set of mirrors and field lenses.
An overhead projector works similarly to a slide projector, but with a Fresnel lens as the field lens.
The idea of using field lenses to avoid light loss can be repeated many times in one instrument to produce an efficient periscope or cytoscope.
Exam I Thursday Oct. 18 at 6:30pm in Hasbrouck 126
In this section of the course we study the operation of the camera and some of the technical features of photography, applying much of what we have just learned about optical instruments. In the next section of the course, we go on to draw a number of analogies between the eye and the camera.
Reading: STL Chapter 4 -- sections 4.1-4.6
Section 4.1 outlines the important parts of the camera. Section 4.2 defines "depth of focus" and discusses different focussing arrangements and rangefinders. Section 4.3 discusses the effects of objective focal length in terms of field of view, magnification and perspective, while section 4.4 talks about different types of camera lenses. Section 4.5 covers the devices that control light input (exposure): shutters and apertures while section 4.6 defines the term "exposure" in a precise mathematical sense.
Optional Reading: STL Chapter 4 -- section 4.7
Those of you really interested in photography may want to read the last section of chapter 4, which discusses some of the details of film and film processing. We will only briefly cover this in class.
Optional Reading: "The Camera" by Ansel Adams, on reserve in the Physical Science Library.
An excellent practical introduction to the camera for the would-be professional photographer.
The lens of a camera must be focussed for different object distances and it introduces the problem of dispersion of different colors of light, but in return it allows the camera to gather much more light than it would with a pinhole. Color dispersion is alleviated somewhat by the use of achromatic lenses: two or more lenses of different indexes of refraction for which the dispersion from each lens partially cancels.
The interchangable lenses of different focal length on a modern SLR camera allow the photographer to adjust the field of view and the magnification of the image on the film. Long focal length lenses (often called "telephoto") provide high magnification while short focal length lenses ("wide angle") provide a large field of view.
Interestingly enough, a closeup photo with a short focal length lens cannot be made exactly identical to a distant photograph with a long focal length lens. The subtle difference is a matter of "perspective", which we will explore briefly.
In order to focus a camera at different distances, we need to adjust the distance between the lens and the film. This is in contrast to the focussing mechanism in the eye, in which the shape of the lens is changed. We will notice that as the object distance becomes larger, the image distance (the distance between the lens and the film) changes less and less. This feature is a natural consequence of the lens equation we learned earlier, and it relates to the notion of depth of field, which we get to shortly.
Since short and long focal length lenses provide different advantages to photography, most photographers want to have a range of focal lengths at their disposal. One way to accomplish this is with a large collection of lenses. Another alternative is a "zoom" lens, a compound lens that can change its effective focal length. We will look at a couple of examples in class.
Objects at different distances cannot simultaneously be focussed on the film plane. The range of distances that give acceptably sharp images is known as the depth of field, and is controlled by the use of apertures.
Apertures (the openings that let the light through) are measured relative to the focal length of the lens. The ratio of the two is called the f-number. The aperture controls both the amount of light entering the camera and the depth of field for the photograph. A large opening lets in a lot of light but gives a narrow depth of field. A small opening (such as a pinhole!) give a large depth of field but lets in very little light.
The "exposure" of a photograph measures the integrated amount of light hitting the film. As the aperture of the lens is made smaller, the intensity of light on the film goes down and the photograph must be exposed for a longer period of time. The shutter is the device that controls the exposure time, thereby adjusting the darkness/lightness of a photograph and simultaneously affecting the action-stopping nature of the shot. We will look at a few examples of speeding bicycles.
In this course we do not go into the details of film developing (that is more sensibly left to a practical course in photography) but it is useful to at least learn the basic physics and the important terms in film developing, such as emulsion, developer, stop bath, and fixer.
Have you ever wondered how that split circle in the center of a SLR camera works to help you get the right focus? Amaze your friends with your eloquent exposition on split prisms and Fresnel field lenses to explain the operation of a viewfinder.
In this section of the course we get a basic introduction to the anatomy of the human eye. These anatomical features help to explain some of the characteristics of visual perception, which we will study next.
Reading: STL Chapter 5 -- complete
Section 5.2 outlines the various parts of the eye and compares them to similar parts of the camera. Section 5.3 concentrates on the retina and the photochemical processes that take place there.
That small black opening in the center of your eye is what allows the light in. It constricts or dilates over a range of about 1.5 to 8mm, depending on light levels, focussing, and even emotional state. The size of one pupil even depends on the light entering the other pupil. Explore this by shining a flashlight in one pupil while observing the response of both pupils in a mirror.
The retina acts as the projection screen of the eye. It contains several layers that perform different functions. From the outside in, there is the choroid with its antireflective coating, a layer of photosensitive cells (photoreceptors), and several layers of neurons connecting the photoreceptors to nerve fibers, which carry the signals to the brain. The innermost layer is made up of a network of blood vessels that cover almost the entire retina and bring the necessary nutrients to the retinal cells. The red eyes often seen in flash portrait photography are due to the flash reflecting off the blood vessels in the retina.
Focussing of light takes place both at the cornea and at the eyelens. The cornea provides the stronger power lens but is fixed and inflexible. The adjustable eyelens is what allows the eye to focus for different distances. This amazing piece of engineering is suspended in the fluid of the eye and held in place by thousands of fibers that control the tension and the shape of the lens. As the eyelens ages, it grows new cellular layers (not unlike the layers of an onion) and becomes less malleable. Older people therefore have less flexible eyelenses and are often farsighted.
The many reflecting surfaces inside the eye (both sides of the cornea and both sides of the eyelens) can be discerned by looking at reflections in the eye called Purkinje images, named after Johannes Purkinje (1789-1869).We will look at reflections of a candle flame in each others eyes (being very careful about eyebrows) and use what we know about spherical mirrors to understand the shape of the reflecting surfaces that produce them.
Your eye is constructed more like a water-filled balloon than a hard sphere. The aqueous and vitreous humors are the fluids that fill the eyeball. In addition to providing the pressure to hold up the eye, they also transport nutrients to the eyelens and cornea. Some people suffer from a condition known as glaucoma, in which the fluid pressure in the eye is so high that it slowly damages the retina, causing tunnel vision. You can sometimes see evidence for fluid in your eye by looking for the shadows of dead blood cells ("floaters") on your retina.
Where the optic nerve exits the eye there is a blind spot in the retina with no photoreceptors. Most of the time your brain does not notice the missing vision, but you can locate your blind spot by holding a pencil at arms length in front of you and moving the pencil slowly to the side (while looking straight ahead) until the tip of the pencil disappears. Charles the second was said to eliminate the heads of his courtiers in this way.
The choroid lies just outside the retina. It contains a network of capillaries that tranport blood cells to the humors of the eye. It is coated on the inside with a pigmented layer that absorbs light and eliminates reflections back into the retina. Some nocturnal animals replace this pigment layer with a reflective later (the "tapetum lucidum") to increase light on the retina in low light conditions. This is why many animal eyes reflect brightly in your car headlights.
The photoreceptor cells convert light energy into chemical signals read by the brain. There are about 130 million photoreceptors in a human eye, each a couple of microns in diameter. This makes for a couple hundred times more pixels than your average computer screen. These photoreceptors are connected to about a million nerve fibers. A human has four types of photoreceptors, three types of "cones" for daytime color vision and one type of "rod" for night vision. Some nocturnal animals have only rods; some diurnal animals have only cones.
The fovea is a small depression in the center of the retina where there is a very high density of photoreceptors. This region of the retina is where you have the most acute vision. Rabbits have what is called a foveal strip across the center of the retina so that they have acute vision all across the horizon.
Photoreceptors contain photosensitive chemicals composed of retinine (a pigment) and proteins. The different chemicals in the rods and three types of cones are sensitive to different colors of light, allowing the brain to differentiate color. The time for chemical processing and replacement governs response times and dark adaption time for the eye. You will notice that it takes 10-20 minutes in a dark room for your eyes to replace the used chemicals in your eye so that you are fully sensitive. In this state, your eyes may be thousands of times more sensitive than they are in the noonday sun.
Since it takes some time for the chemical processes in your eye to take place, there is a short lag time before your brain can process the light that enters your eyes. This is effect is referred to as "latency". It also takes a short amount of time for the chemicals to quit flowing even after the light is turned off. This effect is referred to as "persistence". Persistence is what makes discrete movie frames appear as continuous movement.
Many aspects of visual perception are explained by specific features of anatomy of the eye. We explore some of these connections between anatomy and perception in what follows.
Reading: STL Chapter 7 -- 7.1-7.2, 7.4-7.7; Chapter 8 -- sections 8.1- 8.6
Section 7.2 gives describes the neurology of the human visual system. We will skip section 7.3 on Weber's law. We pick up with section 7.4, which describes lateral inhibition and its results in terms of lightness constancy, lightness contrast and edge processing. Section 7.5 explains how desensitization leads to negative afterimages and section 7.6 describes eye movements and how they suppress desensitization. Section 7.7 talks about latency and persistence in human visual chemistry and how they lead to positive afterimages.
Chapter 8 deals exclusively with the features of depth perception. Sections 8.2 to 8.4 cover accommodation, convergence and parallax. Parallax is closely related to binocular disparity, described in section 8.5, which explains the operation of stereograms. Finally, section 8.6 constructs the list of ambiguous depth clues and discusses how many of them can lead to optical illusions.
The structure of the retina defines the ultimate resolution and the sensitivity of the eye. The photoreceptors (rods and cones) are connected to bipolar cells, which in turn are connected to ganglion cells, which in turn connect to the optic nerve leading to the brain. Typically, many rods and cones connect to a single bipolar cell and many bipolar cells connect to the same ganglion cell. In all, there are about 100 million photorecptors and about a million ganglion cells. In the network there are also many cross-connections so that a single photoreceptor may connect to more than one ganglion cell. The layout of these connections explains many features of human visual perception.
One important feature of the retinal network is that a direct connection from a photoreceptor to a ganglion cell provides a positive (bright) signal to the brain while a cross-connection to a neighboring ganglion cell inhibits the ganglion cell, providing a dark signal. This surprising feature accounts for two interesting phenomena in visual processing: lightness contrast and edge enhancment.
The perceived shade of an object depends on the brightness of the surrounding visual field. A certain shade viewed with a surrounding bright background will appear darker than the same shade viewed with a surrounding dark background.
The process of lateral inhibition makes the neighborhood of a dark object appear lighter and the neighborhood of a light object appear darker. This leads to better contrast near boundaries of light and dark. As a result, human eyes (and brains) are very good at processing edge information. The effect is especially striking in the black and white television test pattern, which we will examine.
The retinal response to light is inherently a chemical process. There are two important consequences of this. The first is that the chemicals in the retina can be temporarily depleted following exposure to light, giving rise to a period of desensitization. (This desensitization makes it hard to notice some static images in your eye, such as the shadows of blood vessels on your retina.) The second consequence is that none of the chemical transfers start or stop instantly and, in particular, chemicals can continue to flow for a short time after the light has been turned off.
Desensitization occurs in localized regions on the retina, whereever there is a bright image. If the light is removed and the retina is exposed to a uniform illumination throughout, the region of the former bright image is less sensitive than the surrounding area and will produce the appearance of a dark image. This effect is called a negative afterimage, and it sometimes lasts for many seconds.
Positive afterimages can also be present for very short periods of time (up to 1/20 of a second). These result from the continued flow of chemicals in the retina even after exposure has stopped, an effect known as "persistence". These short duration positive afterimages make the sequential images in a movie film or on a television screen appear continuous.
Desensitization also causes stationary images to slowly disappear from the visual field. If you were capable of holding your eyes perfectly still, and were staring at an unchanging view, your entire visual field would slowly fade to a uniform gray. Fortunately, your eyes are constantly moving (even when you don't want them to) in order to change the visual field and keep desensitization from being a problem.
Surprisingly, there are many other types of desensitization within the brain, which affect how you perceive motion and patterns. We will not explore this in much detail but it is interesting to note, for instance, that your perception of speed and motion can be desensitized so that for instance, after driving on the highway for a long time, when you get back on city streets you will seem to be going much slower than you really are.
There are a number of different aspects to depth perception. These natually divide into two broad classes: aspects that rely on physiological features of the eyes, and aspects that are perceptive depth clues (which can mimicked even in 2D representations).
Accomodation is often loosely called focussing. It describes the adjustment of the eyelens necessary to focus on objects at different distances. Your brain notices the tension in your eye muscles and can infer some measure of depth as a result. This works best only at short distances.
Convergence requires two eyes with overlapping visual fields. It refers to the angle your eyes have to cross in order to both see the same object. Once again, your brain can use this information to get a rough estimate of distance, and once again, this depth clue works best at short distances.
Parallax (or specifically, binocular disparity) describes the slightly different viewpoints of the two eyes in their different locations. Your brain tries to interpret the different viewpoints by assigning depth to the picture. This is perhaps the most powerful depth clue used by humans.
Parallax is also the trick used by stereoscopic photographs and by stereograms in order to convey a sense of depth in a 2D picture. A stereoscopic photograph is a pair of photos taken from slightly different positions (just as they might appear to left and right eyes). When each photo is presented to the corresponding eye, usually with the aid of some special glasses, the brain interprets the resulting image as depth. A random dot stereogram uses the same sort of trick but with a repeating pattern of dots. Through careful arrangment and observation, an apparently random field of dots can produce an apparently 3D image.
The Pulfrich phenomenon (named after a man who never saw the effect because he was blind in one eye) is caused by latency in the eyes and produces a form of parallax which results in a false appearance of depth. Retinal cells respond more slowly to dim light (latency). If a dark filter is placed over one eye, its image will lag in time behind the other eye, producing two slightly different images (parallax).
Many depth clues do not rely on binocular vision and are available to artists who work in two dimensions. These clues tend to be ambiguous, and can lead to some interesting illusions.
Self-explanatory. Smaller images on the retina can usually be safely interpreted as due to more distant objects, except of course when it is a small nearby object.
In this context, "perspective" refers to the fact that parallel lines appear to come together in the distance. Perspective is commonly used in art in order to give a sense of depth. Not to be confused with "convergence", which refers to the angle of the eyes.
Most everyone has noticed rays of sunlight (called Bhudda's rays) shining through clouds. They appear to diverge radially from the sun. This natural phenomenon is often depicted in religious paintings. What most people never realize is that those rays are essentially parallel, and that Bhudda's rays demonstrate perspective.
The fact that the atmosphere preferentially scatters blue light changes the apparent color of objects in the distance. Hills in the distance often look as if they are viewed through a blue haze.
Distant objects usually appear less sharp. This is due to the fact that the image on the retina is smaller and produces poorer resolution. Artists often make use of this fact to imply distance.
An extremely powerful depth clue. The image that hides other images under it is due to the closest object. Some very clever optical illusions are based on this principle.
(Mis)use of many of the depth clues just mentioned can result in artwork that depicts impossible objects. We will examine a number of examples in class.
Exam II Thursday Nov. 29 at 6:30pm in Hasbrouck 126
Reading: STL Chapter 1 -- sections 1.2A, 1.3-1.4; Chapter 12 -- sections 12.1-12.2, 12.4B-12.5A
Chapter 1 introduces us to the idea that light is an electromagnetic wave and reviews some of the simple features of waves. Chapter 12 concentrates on two phenomena that are unique to waves, interference and diffraction. Section 12.2 discusses most aspects of interference from thin films, from slits and from gratings. Section 12.4B defines Huygen's very important principle for constructing an arbitrary wave out of a series of point sources. Section 12.5A discusses how light spreads out from a single small hole or slit (diffraction).
The model we have used for light so far is based on the idea of light rays. However, in order to describe some aspects of light, such as color, interference and diffraction, it is necessary to develop a more sophisticated model, a model which incorporates some of the characteristics of waves (such as interference and diffraction). We begin by thinking of light as an electromagnetic wave.
We are familiar with many types of waves that we experience in everyday life. We can see waves on a vibrating string, water waves at the beach, hear sound waves in air. In each case, the waves are generated by the movement of some medium (the string, water molocules or air molocules). It turns out that light is different from any of these other types of waves in that they are not due to the motion of some medium. Light can travel even through the vacuum of space. One way to think of light waves is as a "disturbance of the electromagnetic field". We develop the notion of an electromagnetic field in what follows.
We know that electric charges exert forces on one another. Two like charges (both positive or both negative) will repell each other, while two unlike charges will attract each other. We will verify this in class by putting some static charges on small metal spheres called pith balls.
In the pith ball experiment, the balls feel forces even though the balls are not touching. There is something pulling on each ball even though there is no material object nearby. (This is very similar to gravity.) The something that pulls is what we call the electric field. To describe this electric force we often imagine electric field lines emanating from an electric charge, telling us what direction a positive test charge would be pulled if we were to put it in the vicinity of the that charge.
Magnetic fields can be treated similarly. In fact, the notion of field lines was first introduced by Michael Faraday as they pertain to magnetic fields. Faraday got this idea by looking at how iron filings line up in a magnetic field. We now draw magnetic field lines from north to south poles of a magnet in the same way that iron filings are oriented.
It is useful to think of these imaginary field lines as behaving like stretched strings. They can propogate waves very much like a vibrating string. Whenever we shake an electric charge, the electric and magnetic field lines shake with it, thereby producing waves, which we experience as light. For many purposes, it is useful to think of light as a set of oscillating electric and magnetic fields (waves).
We explore the use of a wave model of light later in the course, but first we review some of the characteristics of waves.
The distance between repeating pieces of the wave.
The time between repetitions for someone sitting still as the wave passes by.
The height of the wave crest.
The location in the repeating cycle of the wave, measured in radians or degrees.
The inverse of "period". Frequency is measured in repetitions/time.
Different frequencies of light correspond to different colors. Moreover, electromagnetic radiation extends beyond what we call visible light into ultraviolet (and higher) frequencies and infrared (and lower) frequencies.
Electromagnetic waves (a.k.a. light) can be generated in any of a number of ways, but all are related to the movement of electric charges. Electrons in a tungsten filament are jostled back and forth in the hot metal, thereby shaking their electric field lines and generating light. Fluorescent tubes and radio antennas behave in a similar fashion. In class, we will light a fluorescent tube without a light socket.
Two or more waves add together by "superposition". To superpose two waves just add their heights at each point. Waves can add together "constructively" or "destructively". Destructive interference is one of the most interesting features of waves. Two identical waves that are competely out of phase will interfere destructively and cancel completely, leaving no wave at all.
If we drop a pebble in a pond, waves propagate outward in all directions. We call these circular wavefronts. Waves that travel in a single direction are called plane waves. (Instead of using a set of parallel light rays to describe a beam of light, think of a set of plane wavefronts with the wavefronts perpendicular to the direction of the rays.)
Christiaan Huygens, a 17th century Dutch mathematician, made the useful observation that any shape wavefront can be produced by a collection (possibly infinite) of point sources that emit spherical wavefronts. This important principle allows a detailed understanding of many features of light. In this course, we will later invoke Huygens principle in order to understand how holograms work.
All of the features of light that we understood within the context of light rays can also be explained by light waves. As an important example, we inspect the laws of reflection and refraction for plane waves using Huygens principle.
It turns out that the phase of light undergoes some interesting changes upon reflection. These phase changes are important for our later understanding of how light reflects off of thin films. We have previously noticed that reflection occurs at any boundary where there is a change in index of refraction. In reflecting off a medium of higher index of refraction, a light wave changes phase by 180 degrees, much like the wave on a string reflecting off an anchored end. Such a reflection is called a hard reflection. In reflecting off a medium of lower index of refraction, no phase change occurs. We demonstrate this idea in class with a Shive machine.
We will explore two aspects of light that cannot be explained in terms of the ray model of light. Both interference and diffraction require features of waves to explain them.
Waves from two or more sources can interfere constructively or destructively, depending on the relative phases of the waves. This fact leads to some peculiar results in Young's double slit experiment, below.
If a wave goes through a very narrow slit (narrow compared to the wavelength of light used), the light spreads out (diffracts) like a point source. This phenomenon is not explained in terms of light rays. However, it is familiar to us as a feature of waves. Water waves traveling through a narrow opening spread out on the other side, as we will see in class. The fact that light diffracts is one reason why we need to abandon our light ray model in favor of a model that is based on light waves.
Previously, we noted that the smaller the pinhole of a pinhole camera, the sharper the image. In truth, that tendency only goes so far. For extremely small pinholes the image becomes fuzzy again because of diffraction.
Thomas Young, working at the turn of the 19th century, demonstrated the interference of light from two slits in a mask. He used these effects to promote a wavelike interpretation of light.
We begin with an easy demonstration of the interference of two sources of water waves. In certain places the waves interfere constructively to produce a wave of large amplitude, while in other places the waves interfere destructively to produce still water.
The same effect can be observed from two sources (slits in a mask) of light. Counter to intuition, it is possible to illuminate a certain point on a projection screen with one source of light, producing a bright spot. Then, when another source of light is turned on, the two sources of light may interfere destructively to produce a dark spot where the bright spot was previously located.
The results of the double slit experiment teach us that light sources can interfere with each other. They can even cancel each other out! Clearly our old model of light using light rays is not capable of explaining these interference effects. This result, in addition to the observation of the diffraction of light, tells us we need to start thinking about light waves.
In Young's double slit experiment, the interference pattern of light on the projection screen depends on the spacing of the slits in the mask.
With three or more slits, the pattern changes in predictable ways. We will exercise our geometry skills to try to figure out these patterns.
The relation between slit spacing, fringe spacing and the wavelength of light allows a means to calculating the wavelength of light by measuring slit and fringe spacings. In class we will effectively measure the wavelength of light with a shop ruler.
Why don't two light bulbs exhibit constructive and destructive interference the same way two slits in Young's experiment did? The answer is in the word "coherence". In order to interfere consistently, two sources must have a constant phase relation, i.e. they must be coherent.
Interference is also the explanation behind the behavior of thin film coatings. Depending on the thickness and index of refraction, a film may be perfectly transparent or maximally reflecting. This fact allows the construction of photographic lenses that do not reflect stray light or sunglass lenses that preferentially reflect certain colors.
An interference pattern can also occur as light diffracts around a water droplet. The pattern looks a lot like laser diffraction through a small hole. Different wavelengths diffract at different angles so a while light pattern will appear as a series of multicolored concentric rings.
Reading: STL Chapter 9 -- sections 9.1-9.2; Chapter 10 -- sections 10.1-10.3, 10.5-10.7
Section 9.2 defines the term "spectral" color, which we need to describe many aspects of color vision. We will return to the remainder of chapter 9 on color models after we understand more about color vision. Section 10.2 introduces the concept of trichromatic vision and presents a thorough description of the experimental data that indicate the response curves of the three types of cones. Section 10.3 tells us how to produce matching color perceptions with different frequencies of light. Section 10.5 describes the different typesof color deficient vision. Sections 10.6 and 10.7 describe the spatial and temporal processing of color, in close analogy to the spatial and temporal processing black and white images, which we discussed earlier.
Thomas Young was also the first person to put forth a three color theory of color perception. Today we understand the three color theory in terms of its anatomical foundation. Biologists have found three types of cones in the human eye that respond to different frequency ranges (colors) of light.
Strictly, a spectral color is a light of a single frequency. However, the perception of a spectral color can often be mimicked by a collection of different frequencies. How that occurs is explained by the three-color nature of human visual perception.
There are many types of color blindness, corresponding to the many different ways in which photoreceptors can be defficient. We will do some standard tests for color blindness in class.
Roughly equal stimulation of all three types of cones in the human eye is perceived as a neutral color (white or grey). Two colors are called complementary if a combination of the two produces white.
Lateral inhibition, which we discussed earlier, operates independently for each type of cone. In analogy to the effects we discussed in black and white, color lateral inhibition leads to colored edge enhancement where dissimilar colors meet, color constancy independent of illumination, and simultaneous color contrast.
Latency, persistence and desensitization also occur independently for each type of cone. As a result, both positive and negative afterimages occur in color as well as in black and white.
Assimilation is a new effect that we did not discuss in black and white perception. Assimilation refers to the perception of more than one finely intermingled color as a single color. It is explained by size of the receptor field that determines color compared to the receptor field that determines detail.
The text discusses many clever experimental tests that are done to determine the precise response of each type of cone to different frequencies of light. We will outline some of these tests in class.
Reading: STL Chapter 9 -- sections 9.3-9.6
Section 9.3 defines the important terms "hue", "saturation" and "brightness" to describe the perception of color. Section 9.4 describes additive color mixing and the very important "chromaticity diagram" for specifying a color. Sections 9.5 and 9.6 list the various methods of color mixing, both additive and subtractive.
How do we quantify the visual response to color in a way that is useful to artists? One common method is the chromaticity diagram. Through careful construction we can plot the relative response of three types of cones on a single 2D diagram. We will spend a fair amount of time in class understanding this important tool.
Instead of describing a perceived color in terms of the response of three types of cones, it is sometimes useful to talk in terms of three other quantities: hue, saturation and brightness. We will learn how these quantities are portrayed in a chromaticity diagram.
The theory of additive color mixing applies to the color combination achieved in televisions or computer monitors. It has a simple interpretation in terms of a chromaticity diagram.
Subtractive color mixing applies to color combinations achieved through filters, dyes or inks.
Most people would expect that many identical colored filters stacked on top of each other would produce simply a darker color. In truth, some filters can actually change hue as they are stacked. We will understand this amazing result in terms of our model of color perception and the transmission function of filters. A painful historical example of the danger of filters will be demonstrated by the story of the U.S.S. Trigger at Midway Island.