# Optics for Beginners

## Introduction

Optics is the science of light. If you know nothing about optics, this page (and those linked to it) will explain the basic facts needed to understand how mirages, green flashes, and other refraction phenomena work. A little background is required, so please be patient.

Traditionally, optics is divided into two main areas: geometrical optics, which deals with how light moves and where it goes; and physical optics, which deals with the nature of light itself (which we don't need to get into here) and with the interaction between light and matter (which we will need to use a little bit).

There are also several related fields, like vision, and the science of color. One of these is atmospheric optics, which deals with how light interacts with our atmosphere. Mirages and green flashes are part of atmospheric optics; but you need to understand some basic optics first, before you can understand what air does to light.

Two kinds of optical phenomena are involved in green flashes and mirages:

• atmospheric refraction
• atmospheric transmission

Refraction belongs to geometrical optics; transmission belongs to physical optics. Let's look at both of these fields.

## Geometrical Optics

#### Reversibility.

People often talk about a “line of sight” between two points. Here are two observers, located at points A and B:

If A can see B, then B can see A along the same line of sight, but in the opposite direction.

Most people are aware that the line of sight is the same for both observers; light passes from A to B along the same path as from B to A. We say the light is reversible. Sometimes it is handy to trace the path of the light away from an observer, even though the light is actually moving toward the observer. Reversibility makes this process valid.

#### Rectilinear propagation.

I drew a straight line between A and B in the drawing above, and people usually think of lines of sight as being straight lines. A basic idea behind geometrical optics is that “light travels in straight lines”; but there is a catch to this statement. Light only travels in straight lines in a perfectly uniform medium, like a vacuum. But real transparent materials, such as air, water, and glass, always have small internal variations in their optical properties that bend the path of the light. So light doesn't quite travel in straight lines in real materials.

Particularly, light doesn't travel in straight lines in air, because air isn't uniform: its density varies from place to place, especially at different heights. The variations in density with height are very important in atmospheric refraction, because they make light travel along curved paths, not straight lines, in air.

#### Rays and beams.

There is another catch to the “straight lines” statement. Lines are a geometric idealization; they have no width. These straight or curved “lines” along which light moves are usually called “rays” in optics. Like the lines of geometry, they are a convenient fiction: there really is no such thing as a “ray of light.” Instead, what exists in the real world is a beam of light; and beams have width.

Right away, I should caution you that what I call a beam of light may not be what you call a beam of light. You probably think of something like a searchlight beam, all lit up and plainly visible. But that searchlight beam is only visible because of light that is scattered out of the actual beam. So what you see is not the beam itself, but the path of the beam, made visible by light that is being scattered out of it toward your eye. If the beam were traveling through a vacuum, instead of through polluted urban air, it would be quite invisible. So, remember: I'm talking about invisible beams.

Now, what's the relation between rays and beams? Well, beams are real, and rays are something we imagine. You can think of a ray as the center line of a narrow beam, if you like.

As Mascart says, at the start of the Preface to his great textbook (Paris, 1889) on optics:

A first glance seems to show that, in a homogeneous medium, light is propagated in straight lines, and that the direction of these rays changes suddenly, according to determinate laws, at the surface of separation of two different media. From this point of view, one can build a special science in which one extracts from simple questions of Analysis the study of bundles of rays originally emanating from a single source. However, experiment easily shows that the ray of light has no physical existence and that it vanishes if one tries to isolate it; it is impossible to know the real properties of bundles of rays and of the images they produce in optical systems without introducing the dimensions of the apertures by which they are limited.

It's usually more convenient to talk about rays rather than beams. And the idea of rays is so useful, and so central to geometrical optics, that we often speak of rays as if they really existed, and even say “ray optics” instead of “geometrical optics.”

#### Refraction

The bending of light rays by the varying density in the atmosphere is called atmospheric refraction. Refraction is the basic process that produces both mirages and green flashes; but it requires a separate Web page to explain properly.

There is an exact mathematical law that describes the paths of rays through media with any given properties; so we can compute the path of a ray very accurately. This business of “tracing rays” through the air, or through an optical system, is what geometrical optics is all about.

But it has limitations: when obstacles or apertures are very small, the (actual) wave nature of light makes very narrow beams or shadows spread out and become fuzzy at the edges. Then the wide-beam assumptions that lie beneath geometrical optics are no longer true, and “ray-tracing” fails. As we have had to mention the “nature of light” here, this brings us to physical optics.

## Physical Optics

We need to use the part of physical optics that deals with the loss of light from a beam. There are two main processes:

• absorption
• scattering

#### Absorption.

Light that is absorbed disappears completely, and is (usually) turned into heat. Dark-colored surfaces absorb most of the light that falls on them. (Think of how hot asphalt paving gets on a sunny day.) Air absorbs a little of the light; but air molecules absorb only at particular wavelengths in the spectrum.

The absorptions that are most important in producing green flashes are those in the yellow and orange part of the spectrum, caused by ozone and water vapor. These absorptions are fairly weak; but when the Sun is near the horizon, the path of the sunlight through the air is long enough that most of the yellow and orange light is absorbed. In fact, during twilight, the blue color of the sky overhead is mostly due to absorption of orange light by ozone.

But the blue sky of daytime has a completely different origin: it is due to scattering.

#### Scattering.

Scattering changes only the direction of light. Of course, a mirror does that, too; but what we mean by “scattering” is not simple reflection, which changes the direction of a beam without making it broader; but a re-distribution of the light in all directions.

Rough surfaces scatter light. But air, and the particles suspended in it, also scatter light. The sky is blue because air molecules scatter blue and violet light much more strongly than the colors with longer wavelengths, like yellow and red. Wherever you look in a clear sky, you see blue light that has been scattered toward your eye from the air along your line of sight. The scattering produced by air molecules alone is called “Rayleigh scattering” because it was first explained by Lord Rayleigh, in 1871.

Rayleigh scattering requires particles that are “small” compared to the wavelength of light. Air molecules are roughly a thousand times smaller than visible wavelengths, so they certainly satisfy this requirement.

Larger solid or liquid particles suspended in the air — usually called “dust” or “aerosol” particles — also scatter light. But particulate scattering is mostly into directions near the original direction of the light; so it appears brightest in the part of the sky near the Sun. The bright aureole around the Sun seen in all but the clearest air is caused by this “forward scattering” by aerosols.

Particle scattering is also much more neutral in color than molecular scattering; so the aureole (due to particle scattering) is nearly white. If there is a lot of aerosol scattering, the sky looks whitish instead of a clear blue. And aerosol scattering between you and the distant landscape produces a bluish-white haze, which can even hide objects some distance away. (Because some mirages only appear if the miraged objects are many miles or kilometers away, these mirages will not be seen if there is too much scattering.)

If the particles are only a little larger than the wavelength of light, they scatter almost equally in all directions. The larger the particles, the more the scattering favors the forward direction. And if the particles are large and spherical — raindrops, in fact — the scattering is very selective in certain directions. That's why raindrops produce rainbows.

Other phenomena of atmospheric optics that require aerosol scattering are crepuscular rays, and iridescent clouds. And don't forget that searchlight beam!

#### Extinction and transmission.

Together, the processes (absorption and scattering) that remove light from the beam incident on the atmosphere are called extinction. The light that is not removed from the beam by extinction is transmitted. The fraction of the original light that is transmitted is usually called the transmittance.

When you look directly at the setting Sun, you see its image by the transmitted light. The light that was absorbed is completely gone; the light that was scattered by the air between you and the Sun now lights up the sky.

In air, scattering is the major component of extinction; so the main effect on the low Sun is to scatter the shorter (bluer) wavelengths all over the sky, leaving mostly the longer (redder) wavelengths in the direct beam. So the setting Sun is red, or at least orange. (So is its aureole, because the forward-scattered light has passed through nearly the same amount of air as the directly-transmitted light.)

That doesn't mean that no other colors of light are transmitted at all. But yellow light is transmitted less than red; green, less than yellow; and blue and violet, least of all. Because aerosol extinction is slightly greater for the shorter wavelengths, polluted air transmits even less of the green, blue, and violet light than clear air does.

If the scattering is so strong that the green light in the sky is brighter than the transmitted green light in the direct beam from the Sun, you won't be able to see a green flash.

(A more technical description of extinction is also available.)

## What's Next?

If you have read this far without jumping ahead to the Refraction page, please go there now. It explains how refraction works, and how atmospheric refraction can be calculated very accurately, given a definite atmospheric model (e.g., the distribution of temperature with height.)