Unit 7: Optics
An optical phenomenon involves an interaction between electromagnetic waves and matter. The complete study of optics involves complex mathematics, a thorough understanding of both classical and quantum optical effects, and a great deal of engineering.
We begin by applying simplified models to develop a basic understanding of how optics works, without having to remember all of Maxwell's equations. In geometric optics, we ignore all the effects that are germane to waves, such as interference. This will nevertheless allow us to understand a large variety of phenomena. We will return to the complexities of wave physics as related to optics in the section on wave optics at the end of this unit.
Completing this unit should take you approximately 11 hours.
7.1: Geometric Optics – The Ray Aspect of Light
Light can travel from a source to another location via three ways:
- It can travel directly from the source through empty space, such as from the sun to the earth;
- It can travel through various media, such as through air or glass;
- It can be reflected, such as by a mirror.
In all of these cases, it is possible to almost completely ignore the fact that light is a wave – in particular, we never have to mention the concept of frequency (except indirectly in a quantity called the refractive index, which characterizes the medium).
Geometric optics is essentially the study of all optical phenomena that are independent of light frequency. In an even more simplified version of geometric optics, we also assume that all media through which the light travels are uniform. For example, air is assumed to have uniform density and temperature. Then Maxwell's wave theory predicts light waves transport energy in travels in straight lines, or rays.
Our textbook uses this narrow definition of geometric optics – but you should be aware that light rays can in fact bend, for example when forming a mirage in non-uniform layers of air. Light rays that can bend are part of geometric optics, too! After all, geometry is literally named after a curved object (the Earth).
However, we will only be discussing the geometric optics of light rays that are mostly straight. Such a ray can only change direction when it encounters an object, such as a mirror, or when it passes from one material to another, such as from air to glass, but it then continues in a straight line.
7.2: Geometric Optics – The Law of Reflection
When light hits a smooth reflective surface, it bounces off like a tennis ball, making the same angle on the way out as on the way in, measured relative to a line perpendicular to the surface.
7.3: Geometric Optics – The Law of Refraction
You may remember that the speed of light has its own symbol, c, because we said it is a universal speed for all electromagnetic waves. However, that was only true as long as the light waves propagate in a medium that does not interact in any significant way with the electromagnetic fields that make that wave. More precisely, c is the value of the speed of light in a vacuum! It is c = 299,792,458 m/s (meters per second): a very fast speed indeed.
However, just like sound waves have a different speed in air and in water, so does light. Refraction of light occurs when it crosses the interface between two different materials where the speed of light is different. These material-dependent speeds have been tabulated for many materials.
7.4: Dispersion and Prisms
The speed of light is dependent not only on the material, but also on the frequency of the light in that material. Really the only way to avoid a frequency-dependent speed of light is to have a complete vacuum – which is unrealistic in everyday life.
7.5: Image Formation by Lenses
Geometric optics is the backbone on which our own visual system is built. Seeing an object requires forming a "copy" of the object on the retina of your eye, where light-sensitive cells record the intensity of the light. So the first thing that needs to happen is that light rays emanating from any single point on the object that we can see should correspond to light rays converging to one single point on the retina. If that does not happen, then you see a blurry image, and your perception of reality is not as faithful as it should be.
7.6: Image Formation by Mirrors
We just saw how virtual images can appear in the context of lenses. We can also use curved mirrors to create the same types of focussing effects that we just discussed for lenses. We can also identify the same characteristics: focal point, image distance and magnification.
7.7: Optical Instruments
Now, let's apply the optical design principles of the previous sections to the human eye, and to some of the important optical instruments that enhance the capabilities of our eyes. The lens of our eye is of course not made of glass, but the material does not really matter for the optical principles we have learned so far.
In geometric optics, the material is taken into account entirely within the index of refraction. Most of the human lens is composed of transparent cells, which means the shape of the entire lens is flexible. This gives us the ability to change the focal length of the lens in a process called accommodation, to bring objects at different distances into focus on the retina.
7.8: Wave Optics: Interference
The approximations of geometric optics can also break down for light waves, but this happens at a small size scale because the wavelength of, say, visible light is shorter than about 0.8 micrometers. In this regime, we have to return to Maxwell's insight that light is actually a wave phenomenon. Because of its wave nature, light can therefore show all the effects that other waves show, too.
7.9: Wave Optics: Diffraction
The idea of interference is also behind Huygens' principle, a construct that allows us to build up wave fronts of practically-arbitrary shapes from the interference of many circular elementary waves. This interpretation is of value because it contains one of the most fundamental ideas in physics: the principle of causality. What a wave does at a given point in space is caused in a simple way by what the wave was doing at an earlier time in a neighboring region of space.
In the previous video, Greg Clements also covered a property of light that truly distinguishes it from sound waves or even water waves: polarization. This property is directly related to what we learned in the study of Maxwell's equations and electromagnetic waves: like all traveling waves, light has a direction of propagation in which it transports energy, but it also has another direction we do not usually perceive: the orientation of the electric field, and therefore the orientation of the forces that this wave would exert on a movable charge such as an electron.
At any given point that the wave passes through, the electric field is perpendicular to the propagation direction, and we know that the electric field also oscillates in time. The amplitude of the oscillation defines how much energy the wave carries, but we have not said much about the direction in which this oscillation happens.
While the electric field oscillates, its maxima also moves forward at the speed of light. A graph of the wave, traced out by the electric field, looks a lot like a wave on a rope, or a slinky. That is, the entire wave motion occurs in a plane that contains the direction of propagation as one axis, and the direction of the electric field as another axis.
Let's say the wave is traveling in the horizontal direction, from left to right. Imagine the plane of the electric-field wave as a knife blade, with the long edge of the blade pointing in the propagation direction. Then you can still tilt the blade in many different ways, such as vertically, horizontally, or at some angle in between (without changing the direction in which the long edge points). The tilt angle defines the direction of polarization.