Optics, the study of visible light, is one of the earliest branches of science.  An introductory physics class will usually highlight what happens when a light ray encounters a new medium.  That is, a light ray may be travelling in a straight line unperturbed through medium 1, air, when it suddenly encounters medium 2, a thick plane of glass.  Before the light ray strikes the boundary, it is referred to as an incident ray.

The incident light ray will divide itself upon striking the new medium: some of the ray will reflect, and some of it will refract.  The reflection of a light ray is simple - it is no different than what happens to a billiard ball when it strikes a band.  Just as a billiard ball rebounds off of the flat border with an angle equal to that which it struck with, the angle of the reflected ray is equal to the angle of the incident one.

However, light can also permeate the new medium (an ability that no billiard ball possesses).  The portion of the light that passes through the boundary, continuing its travels into medium 2, is referred to as the refracted ray.  As shown in the figure below, the angle of each ray is measured with respect to an invisible 'normal' line, which is drawn perpendicular to the surface.

The law of reflection says that Ɵ1’ = Ɵ1, which is a fairly intuitive result.  The law of refraction, commonly referred to as Snell's Law, is not nearly as trivial; it says that light bends.  

To fully appreciate the reason for which light bends when it crosses a boundary into a new medium, we need to assign a parameter to each medium.  This parameter, the index of refraction, n, is essentially a measure of how much of a deterrent a given medium is for a light ray.  If a given medium has a high index of refraction, then light will travel significantly slower in that medium that it would in a vacuum.

More specifically, v = c/n, where v is the speed of light in a given medium and c is the speed of light in a vacuum (approximately 300,000 km/s).  The index of refraction in a vacuum is exactly 1, whereas for air, n is just slightly higher than 1 (about 1.0003).  However, for water, n = 1.333, and so light travels at a ratio of 1/1.333 the regular vacuum speed (about 25% slower) in water: just 225,000 km/s.  A medium like glass represents an even greater hindrance for the passage of light, with an index of refraction around 1.5 (it slows down light to the lethargic speed of 200,000 km/s).


Returning then to the figure above, when a light ray crosses the boundary between air and glass, it slows down.  Although the frequency of the light goes unchanged, its wavelength decreases in proportion to the ratio of the refractive indices.  As the wavelength reduces, the curvature of the wave-fronts become less pronounced (the radii grow), and as a result, the ray has no choice but to bend.

The simple equation describing this bending is given by Snell's Law:

n1sin(Ɵ1) = n2sin(Ɵ2)

This equation leads to a few rules regarding refraction:

1.  If n2 > n1, Ɵ2 < Ɵ1

2.  If n2 < n1, Ɵ2 > Ɵ1
3.  If Ɵ1 = 0, Ɵ2 = 0

The first rule says that transferring to a higher index of refraction (like air to glass) causes a light ray to bend towards the normal line.  This is illustrated in the figure above.  Since the angle shrinks, it is always possible to refract into a medium with a larger refractive index.

Rule #2 says just the opposite.  When a light ray strikes a boundary as it attempts to leave a medium that has a higher refractive index, it bends away from the normal line.  Since the angle grows, there is a spectrum of incident rays that may not refract out into a medium of lower refractive index.  For any two media, there exists a certain critical angle above which there shall be no refraction from high n to low n.  In such a circumstance, the light ray does not come to a stop - it just reflects exclusively; this is known as total internal reflection.

The third and final rule listed above represents the only way that a light ray may cross from one medium to another without altering its course.  For the particular case where light is on a course that is exactly perpendicular to the boundary dividing the two media, the ray will not bend as it crosses over (it will still, however, travel at the new speed prescribed by the new refractive index).

With this introductory information regarding optics, let us now attempt to answer the following question: Do people behave like rays of light when they encounter crossroads in their lives?

I find that in a philosophical sense, Snell's Law is illustrated by people when they attempt to cross a boundary into a new environment.  Let us use the example of a High School graduate who is entering University.

There is no question that the demands on a student increase significantly upon entering University.  As this environment, or medium, requires significantly more attention, and poses a much greater challenge, the refractive index of a University is significantly higher than that of a High School.  As a result, the ray of light that represents this transitioning student will need to slow down and focus, and yes, even study, in order to succeed in this new medium.

Furthermore, this maturing student will undoubtedly shift his or her perspective on life in this new environment.  This can be thought of as a modification of one's direction, or, better yet, as a refraction of oneself.

Eventually, the student will see a new boundary emerge in the distance: the finish line.  To complete university successfully, a student cannot carry him or herself in any which way.  In fact, there is a whole spectrum of students that will not graduate from university for one reason or another.  The line in the sand separating the graduates from the non-graduates is defined by the critical angle.

It is sadly not all that uncommon for a student to bounce around within the prism (which sounds eerily close to "prison") of University.  A student experiencing total internal reflection within the college campus walls can become discouraged.  Perhaps the problem for some students is that they do not slow down enough to learn in this information-dense new environment.  By not adjusting to the new demands, they refuse to refract, and in turn, break Snell's law.

It is exceptionally rare to find a student that can transition from High School to University without making some degree of personal changes.  This is not surprising, as only one ray of light in one million will strike a boundary perfectly perpendicular to it.

In summary, it is easier for light to enter a prism than it is for it to leave.  Correspondingly, it is easier to have a goal than it is to fullfill the obligations it entails.  A very high refractive index correlates to a goal with extremely high demands.  There are media with higher indices of refraction than glass: for diamond, n = 2.42.  The critical angle for light to leave diamond and re-emerge into the air is 24.4 degrees.  Light that hits the interior boundary of a diamond ring at an angle greater than this will merely reflect.  One reason why a diamond ring sparkles so brightly is because light rays have so much trouble escaping.

Before each semester, students ought to plan out their schedules carefully.  To abide by Snell's Law, students need to slow down, and dare I say, devote themselves to learning.  If they choose an appropriate path to pass through the prism of school, they will exit successfully into the real world, refracted.

Light is a funny thing. 

It behaves like an electromagnetic wave (it has a phase - it can undergo interference), yet it also behaves like a stream of particles (it consists of photons, as proven by Einstein's photoelectric effect).  The split personality exhibited by light has bewildered scientists for one hundred years.  And, while we will never see a photon with our naked eye, our eyes would see nothing at all if not for light.  These photons reveal the nature of the matter around us, but keep their own true nature under wraps.

The light that reaches our pupils may come directly from a source or it may arrive after a series of reflections off of other surfaces; either way, the light emanates from a source, like the sun or a light bulb.  Both of these particular sources produce what is known as white light. 

All electromagnetic waves, whether they are radio waves or x-rays, have a wavelength associated with them.  Visible light fills a very narrow band within the electromagnetic spectrum: 400 nm to 700 nm.  All wavelengths in this range correspond to a particular colour.  Violet light has a wavelength of 400 nm, while that of red is 700 nm.  A rainbow will have these colours on either side (violet on the bottom, red on top), and all other colours in between ordered by wavelength.  White light is what you get if you superimpose all colours in the visible spectrum on top of one another.  Black, on the other hand, represents the absence of colour.

With this background information on light, we can properly appreciate why a red sports car looks like a red sports car.  It is less obvious than you might think...

The sun undergoes fusion, a nuclear reaction, which produces, among other things, white light.  These white light rays travel in all directions at about 300,000 km/s.  After travelling a little over eight minutes, some of these white light rays hit the red sports car that sits before you.  Then, something critical happens: some of the white light is reflected by the car's surface, but most of it is absorbed.  In fact, the surface absorbs every wavelength of light with the exception of its own, red, 700 nm.  The 700 nm wavelength of the light is reflected by the surface.  These reflected light rays head off in many directions, including yours.  Your brain interprets this wavelength to be red.

So, while the car may be red, we could not make this deduction if not for a source of light that contains, at a minimum, this particular wavelength.  It is kind of like that falling tree... If an object is not lit up by a source, does it have a colour?

The car's red colour gives it a certain character.  And, while one's personality is more complex than a single data point along a spectrum, colour codes for personality classification are often surprisingly telling.

While some professionals balk at colour code personality tests, some psychologists stand by them.  Colour tests may not be 100% accurate, scientifically speaking (what in psychology is?), but such tests do hold some water.  By contrast, astrology used for fortune telling is about as useful as a cookie of Chinese descent.

There are several colour spectra used to describe personalities; one such spectrum is orange-blue-green-gold.  Each colour corresponds to a set of values, which can go a long way towards understanding, and even predicting someone’s behaviour.  

A typical test will ask some questions about your preferences in life: by answering these, you describe your particular set of values.  Are you someone who values the company of family?  Under stress, would you like to retreat to a quiet place, or would you prefer to vent to a close friend?

Upon completion of the test (there are a number of free ones online) one is assigned one of the four colours, which associates most directly with one’s personal values.  No matter what test I take, I am always coded blue.  The blue personality type tends to value close relationships above all, and enjoys deep reflective and spiritual discussions.  I know this reads like a horoscope does, but it is based on my values (not the position of some random star with respect to our particular Celestial body).

Returning to the white light analogy, a person's colour code is quite irrelevant unless he or she interacts with his or her environment.  Our environment consists of all colours, and the way we react to given situations (how we reflect light) tells the story of who we are.  Ideally, we absorb what we are not, and reflect what we are.  In so doing, we learn to understand others, and teach others to understand us.  However, unlike inanimate objects, people can choose whether or not to project their true colours to the surface.

There is no benefit to hiding behind a facade.  Suppressing who we are causes confusion to those around us, akin to that red car reflecting yellow light.

Can different personality types get along?  I sure hope so (my wife is a green).  Still, people with similar personalities will need to work less hard to understand one another.  Like colours see eye to eye.  Sometimes we say that two such people are on the same wavelength.  Colour-coding people by personality gives a new depth to this statement.

Of course, a gold may help an orange solve a problem, and an orange may help a gold conquer a fear.  Different personality types can often compliment one another in surprising ways; colours of different wavelength are no different.  One can dress in blue from head to toe, but it would make for a fairly bland outfit.  That being said, when different colours interact, there is a risk that they will clash.  But it is a risk worth taking, because more often than not, they create a pleasant contrast.

Living things differ from inanimate objects in their dealings with light in one other key way: in addition to reflecting it, they can project it.  Some indescribable source of light glows from within each of us.  Whatever colour you are, you have the ability to shine it, even in an environment of darkness.

We still have much to learn about the behaviour of light, and of course, as much or more to learn about ourselves.