Polarised light and unpolarised lightmeaning

A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

A quarter-wave plate δ = π/2 can be used to convert linearly polarized light to circularly polarized light.  The incident linearly polarized light must be oriented at 45o to the wave plate's axes.  A half-wave plate δ = π can be used to rotate the plane of linearly polarized light.  The angle of rotation is 2θ, where θ is the angle between the angle of polarization and the wave plate's fast axis.

An inverted, or inside-out mask of a face looks very strange to us.  If we move past it, or the mask moves by us, it will appear to turn its head to look at us.  This is because of “paralax”.  Just like how distant trees appear to move by slower than closer trees as we drive through a forest, the nose of the mask will not appear to move as much, because it is farther away.  The sides of the face on the mask will appear to move more because they are closer.  However, our brain is very good at seeing faces, even where there are none, such is in clouds.  Your brain is easily tricked into seeing the inside-out mask as a face, with its nose closer to us and the ears farther away.  The only way your brain can match this with the relatively slow turning nose and more rapidly turning ears is that the face must be turning to follow you.  This trick is also used in the “Haunted Mansion” in Disneyland and Disney World.

Unpolarizedlightexamples

In other devices the changes in direction of propagation between the two rays is used to separate the incoming beam into two orthogonally polarized beams as in the Wollaston and Thompson beam-splitting prisms.

Red objects are red because they reflect red light and absorb, or soak up, all other colors.  Blue objects are blue because they reflect blue light and absorb all other colors.  If you only shine blue light on a red object, it will appear black, and if you shine only red light on a blue object it will also appear black.  This also works with the other colors.  If the color of the light shining on an object with many bright colors is quickly changed, it can look pretty freaky.

Wave a white rod or board back and forth through the beam from a slide or video projector very fast.  It will look like the whole image or screen even though only a bit of the image that hits the rod or board can be seen at any instant.

Unpolarizedlight

When the sun is at a low angle in the sky, the sunlight reflecting off the surface of water is nearly 100% horizontally polarized because the angle of incidence is close to the Brewster angle.  Glare-reducing sunglasses are coated with a polarizer with a vertical transmission axis and therefore block the reflected light.

Plane polarizedlight

Light given off or absorbed (soaked up) by a gas is unique, like a fingerprint.  We can tell what elements and chemicals are in a gas by the colors of light (called a “spectra”) it gives off.  Pure elements give off very clear patterns of colors.  We use this to determine what elements and chemicals are in far off stars, in the atmosphere of distant planets, and in giant gas clouds in outer space.

Linear polarization

Very few things are cooler than lots of lasers shining through fog and mist to make pretty patterns, especially if lots of students can help out!

In the Glan-Taylor polarizing prism shown on the right the rejected (ordinary) ray is absorbed by black mounting material in the prism housing.

A popular magician’s trick is called “Pepper’s Ghost”.  Light will bounce off of clear flat glass as well as pass through it.  If the light is just right, you can see things reflected in the glass as well as things on the other side of the glass.  If two objects are placed on opposite sides of the glass so the are right where the reflected image of the other is, what you will see is both objects together, apparently in the same place.  You can use this to make an unlit candle appear to be lit, or to even burn under water.  If you start with one of the objects in darkness, and then shine a light on it, its reflection will “magically” appear in the glass.  This trick is used many times in the “Haunted Mansion” in Disneyland and Disney World to make “ghosts” appear and disappear.

When light goes from one material to another, it bends.  A laser beam that hits water, glass, or plastic will change direction.  Under the water, the beam will look like it came from somewhere else.  Light coming up out of water will also bend, making it appear to come from somewhere else.  This is why straight sticks will appear to be bent when stuck into water, why fish appear to be farther from shore, and closer to the surface than they really are, and why streams do not look as deep as they really are.  If you shine a light straight down at water, most of the light will go into the water, and some will reflect.  The same thing happens if light is coming out of water into air.  However, if the light inside the water hits the air at larger and larger angles, more and more of the light is bounced, or reflected, back into the water.  If the angle is large enough, all of the light is bounced back, and none of it will go into the air.  This also happens with clear plastic, glass, and even Jello.  We can use this to make “light pipes” that can carry signals in the form of light over very long distances with very little loss of signal.

The two beams within the birefringent crystal are referred to as the ordinary and extraordinary ray, respectively.  The polarization of the extraordinary ray lies in the plane containing the direction of propagation and the optic axis, and the polarization of the ordinary ray is perpendicular to this plane.

Mostly when light bounces, it does so in all directions, because the surface is rough.  If the surface is smooth enough, like still water, glass, polished metal, or a mirror, the light will only bounce in one direction, like a ball.  It will bounce off at the same angle it hit.  If you shine a laser on a mirror, you can only see the light if you are in the direction it bounces, and then it looks like the light came from behind the mirror.  Unlike a laser beam, light from a normal object, like a light bulb, will hit everywhere on the mirror, so it is much more likely that some of the light will bounce your way.  It will still look like it came from behind the mirror.  This is what we call a reflection.

Polarised light and unpolarised lightdifference

The figure below shows the trace of the field vector Ex = E0exp(i(kz - ωt)), Ey = E0exp(i(kz - ωt + φ)) in a plane perpendicular to the z-axis when looking towards the source.  (E0x = E0y = E0)

It takes time for our brains to understand what our eyes see.  Because of that, a fast moving laser beam spot will not look like a spot at all, but like a line of light.  If a laser beam is moved fast enough, the beam spot on a wall can be made to look like a circle or some other figure.  However, if you took a photograph of it, and if the camera is fast enough, it will clearly show just a spot.  Movies and TV are just a series of still pictures flashed quickly on the screen.  The flashing is fast enough so that it looks like smooth motion to us.

Many colorful toys and lights use light pipes made of glass, called optical fibers.  Fiber optic cables are used to send phone and tv signals in the form of light over long distances.

Water with a little Pine-Sol will scatter enough light to make a laser beam visible.  If a laser beam enters a glass bottle just right so that it leaves through a hole, the laser light will bounce around inside of the water stream coming out the hole without leaving the water.  You can see the laser beam inside the water if there is enough Pine-Sol, or if the water stream hits something.

Polarised light and unpolarised lightreddit

The extraordinary ray violates both Snell’s Law and the Law of Reflection.  It is not necessarily confined to the plane of incidence.  Its speed changes with direction.  The index of refraction for the extraordinary ray is a continuous function of direction.  The index of refraction for the ordinary ray is independent of direction.  When the ordinary index of refraction is plotted against wavelength, the dispersion curve for the ordinary ray is a single unique curve.  The dispersion curve for the extraordinary ray is a family of curves with different curves for different directions.  A ray normally incident on a birefringent crystalline surface will be divided into two rays at the boundary, unless it is in a special polarization state or unless the crystalline surface is perpendicular to an optic axis.  The extraordinary ray will deviate from the incident direction while the ordinary ray will not.  The ordinary ray index n0 and the most extreme extraordinary ray index ne are together known as the principal indices of refraction of the material.  The direction of the lesser index is called the fast axis because light polarized in that direction has the higher speed.

Examples of polarizedandunpolarizedlight

If you look very closely (think face-plant) at a the image on a TV or computer screen, you will see red, green, and blue spots very close together, especially where the image is white.  All colors we can see can be made by mixing red, green, and blue in the right combinations.  An equal mixture of each will look white.  A white rod in red light will look red, and its shadow will look black.  A white rod in green light will look green, and its shadow will look black.  A white rod in blue light will look blue, and its shadow will look black.  A white rod in front of a red light and a blue light will look magenta, and it will have two shadows, one blue, and the other red.  A white rod in front of a red and in front of a green light will look yellow, and it will have two shadows, one red, and the other green.  A white rod in front of a blue and in front of a green light will look cyan (or aqua), and it will have two shadows, one blue, and the other green.  If the rod is in front of a red light, a green light, and a blue light, it will appear white and have three shadows, one magenta, one yellow, and the third one cyan.

In order for us to see an object, light must come from it to our eyes.  Mostly we see light from the sun or other sources that bounces off of objects.  Occasionally, objects emit their own light.  Light travels in straight lines.  A laser produces light, but unless the laser light bounces off of something, or shines directly into your eyes (a very bad idea, since this can damage your eyes), you cannot see it.  The beam is invisible in normal air.  However, you can see the beam if there is something in the air, like smoke, that the light can bounce off of.

Pure white light and sunlight contain all of the colors of the rainbow.  Because different colors of light bend differently in different materials, white light can be split up to form a rainbow by prisms, glass balls, and even special plastic sheets.  Rainbows in the sky are from sunlight bent through and off of millions and millions of raindrops.

There are many colors we cannot see.  Beyond violet we have ultraviolet and beyond red we have infrared.  However, most cameras can see quite well into the infrared, and change it to light we can see.  A camera image of a rainbow clearly shows light beyond red that we cannot see.  It can also see the infrared light signal from a TV remote.

The electric field vector E can always be resolved into two perpendicular components.  The light is elliptically polarized, then the two components have a constant phase difference, and the tip of the electric field vector traces out an ellipse in the plane perpendicular to the direction of propagation.

If a beam of linearly polarized monochromatic light enters a birefringent crystal along a direction not parallel to the optical axis of the crystal, the beam will may be divided into two separate beams.  Each will be polarized at right angles to the other, and they will travel in different directions.  The intensity of the original beam will be divided between the two new beams in a manner which depends on the original orientation of the electric field vector with respect to the crystal.  The ratio or the intensities of the two orthogonally polarized beams can have any value.

Linearly polarized light is a special case of elliptically polarized light.  If the light is linearly polarized, then the two components oscillate in phase,  for example Ex = E0xexp(i(kz - ωt)), Ey = E0yexp(i(kz - ωt)), φ = 0.  The direction of E and the direction of propagation define a plane.  The electric vector traces out a straight line.  For example, E = Ei = E0xexp(i(kz - ωt))i.

Glasses made with special plastic sheets can split light up into colors just like a prism or raindrops.  Different sources of light are fun to look at through rainbow glasses.  A white light bulb gives off all colors, while a white florescent bulb gives off only five distinct colors.