Laser Optics Experiments

You can use lasers for almost any experiments customarily associated with a non-coherent or white light source. E.g., laser light refracts and reflects the same as ordinary light, allowing you to use a laser for experimenting with or testing the effects of refraction and reflection.

Moreover, laser light provides some distinct advantages over ordinary white light sources. The light from a laser—such as a helium-neon tube—is highly collimated. The pencil-thin beam is easily controllable without the use of supplementary lenses. That makes routine optics experiments much easier to perform.

Because laser light is comprised of so much intense, compact illumination, you can readily use it to demonstrate or teach the effects of diffraction, total internal reflection, and interference. When using ordinary light sources, these topics remain abstract and hard to comprehend because they are difficult to show. But with laser light, the effects are clearly visible. You can readily see the effects of diffraction and other optical phenomena using simple components and setups.

This section shows how to conduct many fascinating experiments using visible la ser light. While you don’t need to complete each experiment, you should try a handful and perhaps expand on one or more for a more in-depth study. E.g., the effects of polarization by reflection is a fascinating topic that you can easily develop into a science fair project.

EXPERIMENTING WITH REFRACTION

Recall that refraction is the bending of light as it passes from one density to another. Light bends away from line normal at a dense-to-rare transition; light bends toward line normal at a rare-to-dense transition. TABLE 1 lists the materials you’ll need to carry out the experiments in this section.

Refraction through Glass Plate

You can most readily see the effects of refraction by placing a piece of clear plate glass in front of the laser. The beam will be displaced some noticeable distance. Try this experiment: place a laser at one end of the room so that the beam strikes a back wall or screen. Tape a piece of paper to the wall and lightly mark the location of the beam with a pencil.

Next, have someone place a small piece of regular window glass in front of the la ser. Position the glass so that it's canted at an angle to the beam. The spot on the paper should shift. Mark the new location.

ill. 1. Measuring the deflection of the beam enables you to calculate the refractive index of glass, lenses, and other optical components.

If you know the distance between the glass and wall as well as the distance between the two spots, you can calculate the angle of deflection (see ill. 1). (With that angle, you can then compute the refractive index of the glass; consult any book on basic trigonometry for the formula.) The figure shows how the distance between (A)—glass to wall—and (B)—spot to spot, or deflection—are the equivalent of the adjacent and opposite sides of a right triangle. The illustration shows the particular formula to use to find the angle of deflection: A = arctan(a/b). Use trig tables or a scientific calculator to solve for it.

Try the experiment with different types of glass, plastic, and other transparent materials. Move the paper each time you try a new material. Note that not all glass is made of the same substances, and refractive indexes can vary. E.g., one piece of glass may have a refractive index of 1.55 and another may have a refractive index of 1.72. The two may look identical on the outside but refract light differently. The higher the index of refraction, the greater the distance between the two beams.

Refraction through Water

Bears, eagles, and others of the animal kingdom know a lot about refraction; how else could they catch fish out of lakes and streams with such precision! Because water is more dense than air, it has a higher index of refraction. Images in water not only look closer, but they appear at a different place than they really are. If you don’t take refraction into account, you’ll come up with nothing after throwing your spear into the water.

One easy way to demonstrate refraction in water is to place a narrow stick, like a dowel, in a jar. Fill the jar with water and the stick seems to bend. If the water is a little cloudy (as it often is after coming out of the tap), you can demonstrate the actual refraction of light with a laser. Fill the jar with water. Position the laser above the jar but at a 10 to 15 degree angle to the water line. Turn off the room lights so that the beam can be more readily seen in mid-air (chalk dust or smoke helps bring it out). You’ll see the shaft of light from the laser “magically” bend when it strikes the water.

By dipping a protractor in the water, you can visually measure the angles and compute the index of refraction using the classic formula n = sin i/sin r. That is, the index of refraction is equal to the sin of the angle of incidence over the sin of the angle of refraction (this is often referred to as Snell’s Law). Repeat the experiment with other liquids, including glycerin, alcohol, and mineral oil. Correlate the refractive indexes of these fluids with the glass and plastic from above (you can use Snell’s Law for these materials, too).

Equilateral prisms are most often used to disperse white light (break up the light into its individual component colors). The light from a helium-neon laser is already at a specific wavelength, so it cannot be further dispersed. However, prisms can be used to show the effects of refraction and how the light can be diverted from its original path.

To demonstrate refraction in a prism, place the prism at the edge of a table. Aim the laser up toward the prism at a 45 degree angle. The beam should strike one side and then refract so that the light exits almost parallel to the surface of the table. For best results, you’ll need to clamp the laser in place so that the beam doesn’t wander around.

EXPERIMENTING WITH REFLECTION

ill. 2. The law of reflection.

The law of reflection is simple and straight-forward: the angle of reflectance, in relation to line normal, is equal but opposite to the angle of incidence. As an example, light incident on a mirror at a 45-degree angle, as shown in ill. 2, will also bounce off the mirror at a 45-degree angle. The total amount of deflection between incident and reflected light will be 90 degrees. Materials needed for conducting the experiments in this section are found in TABLE 2.

Front-Surface versus Rear-Surface Minors

Light is reflected off almost any surface, including plain glass. An ordinary mirror consists of a piece of glass backed with silver or aluminum. Light is reflected not only off the shiny silver backing but the glass itself. You can readily see this effect by shining a laser at an ordinary rear-surface mirror. With a relatively large distance between mirror and wall, you won'te two distinct spots. The bright spot is the laser beam reflected off the silver backing; the dim spot is the beam reflected off the glass itself.

Now repeat the experiment with a front-surface mirror. Because the highly reflective material is applied to the front of the glass, the light is reflected just once. Only a single spot appears on the wall (see ill. 4)

Total Internal Reflection

When light passes through a dense medium toward a less dense medium, it's refracted into the second medium if the angle of incidence isn't too great. If the angle of incidence is increased to what is called the critical angle of incidence, the light no longer exits the first medium but is totally reflected back into it. This phenomenon, called total internal reflection, is what makes certain kinds of prisms and optical fibers work.

Consider the right-angle prism shown in ill. 4. Light entering one face is totally reflected at the glass-air boundary at the hypotenuse. The reflected light emerges out of the adjacent face of the prism. Depending on how you tilt the prism with respect to the light source, you can get it to reflect internally in other ways.

ill. 3. A rear-surface mirror creates a ghost beam along with the main beam; a front-surface mirror reflects just one beam.

ill. 4. A right-angle prism allows you to deflect and direct light in a number of interesting ways.

The main advantage of total internal reflection is that it's more efficient than even the most highly reflective substances. Reflection is almost 100 percent, even in optics of marginal quality. Another advantage is that the reflective portion of the prism is internal, not external. That lessens the chance of damage caused by dust and other contaminants.

You can readily experiment with total internal reflection (TIR) using just about any prism. A right-angle or equilateral prism works best. Shine the beam of a laser in one side of the prism. Now rotate the prism and note that at some angles, the beam is refracted out of the glass without bouncing around inside. At other angles, the light is reflected once and maybe even twice before exiting again.

If the prism is poorly made—the glass has many impurities, for example—you can even see the laser beam coursing around inside the prism. This effect is best seen when the room lights are turned low or off. To see the effect of total internal reflection and refraction in a prism, make a tube by wrapping a large piece of white construction paper or lightweight cardboard around the prism. Poke a hole for the light beam to go through and turn on the laser. If the paper is thin enough, you can see the laser beam striking it (looking from the outside). If the paper is thick, you’ll have to look down the tube to see the beam on the inside walls.

Rotate the prism (or the laser and tube) and note how the beam is either refracted or internally reflected. Keep a notebook handy and jot down the effects as the prism is rotated. Use a protractor if you want to record the exact angles of incidence.

Another experiment in total internal reflection uses a lens. A long, single-axis lens (the kind shown in ill. 5 like those used for laser scanning) works the best. Shine the light through the lens in the normal manner. Depending on the type of lens used, the beam will refract into an oval or slit. Now cant the lens at an oblique angle to the laser beam, as shown in the figure. If you hold the lens just right, you should see the laser beam internally reflected several times before exiting the other end. You can see the internal reflections much more clearly if the room lights are off.

ill. 5. A long beam-spreading lens (or something similar) can be used to readily demonstrate total internal reflection. A solid glass rod can also be used.

EXPERIMENTING WITH DIFFRACTION

TABLE 3 provides a parts list for the diffraction experiments that follow. Diffraction is a rather complex subject, thoroughly investigated by Thomas Young in 1801. Young’s aim was to prove (or disprove) that light traveled in waves, and were carried along as particles in some invisible matter (the early physicists called this invisible matter the ether). If light was really made of waves, those waves would break up into smaller waves (or secondary wavelets) when passed through a very small opening (according to Huygens’ principle). The same effect occurs when water passes through a small opening. One wave striking the opening turns into many, smaller waves on the other side.

Young used a small pinhole to test his lightwave theory technique. Light exiting the pinhole would be diffracted into many small wavelets. Those wavelets would act to constructively or destructively interfere with one another when they met at a lightly colored screen. Constructive interference is when the phase of the waves are closely matched—the peaks and valleys coincide. The two waves combine with one another and their light intensities are added together. Destructive interference is when the phase of the waves are not in tandem. A peak may coincide with a valley, and the two waves act to cancel each other out.

What Young saw convinced him (and many others) that light was really made up of waves. Young saw a pattern of bright and dark bands on the viewing screen. The brightest and biggest band was in the middle, flanked by alternating light and dark bands. Bright bands meant that the waves met there on the screen constructively. Dark bands denoted destructive interference.

Making Your Own Diffraction Apparatus

Young’s original experiments have been repeated in many school and industrial laboratories. Monochromatic light sources are the best choice when experimenting with diffraction. A laser is the perfect tool not only because its light is highly monochromatic but that its beam is directional and well-defined.

Use a slit instead of using a pinhole for your diffraction experiments. You can make a high-precision slit using two new razor blades, as shown in ill. 6. You can use al most any type of blade, but be sure that they are new and the cutting surfaces aren’t nicked. Mount the razor blades on a small piece of plastic by drilling a hole in the metal (if there isn’t already one) and securing it to the plastic with 6/32 or smaller hardware. Adjust the space between the blades using an automotive spark gap gauge. A gap of less than 0.040 inches is sufficient.

ill. 6. A single slit made by two razor blades butted close together. Mount the blades on apiece of ¼-inch acrylic plastic. Drill or cut a large slot in the center of the plastic for the beam to pass through.

Shine the laser beam through the gap and onto a nearby wall or screen (distance between blades and wall: 2 to 3 feet). You should see a pattern of bright and dark bands. If nothing appears, check the gap and be sure that the laser beam is properly directed between the two blades. If the beam is too narrow, expand it a little with a lens. Note that the center of the diffraction pattern is the brightest. This is the zero order fringe.

If the fringe pattern is difficult to see, increase the distance between the blades and the screen. As the distance is increased, the pattern gets bigger. If the screen is 10 feet or more away (depending on the gap between the razor blades), the light-to-dark transitions of the fringes can be manually counted. Experiment with the gap between the razor blades. Note that, contrary to what you might think, the fringes become closer together with wider gaps. You achieve the largest spacing between fringes with the smallest possible gap.

Experiments with Double Slits

You can perform many useful metrological (measurement) experiments using a double slit. Follow the arrangement shown in ill. 7. Place a single slit in front of a laser so that it's diffracted into secondary wavelets. Then place a double slit in the light path. The fringes that appear on the screen will be an interference/diffraction pattern similar to the fringes seen in the single-slit experiment above. With the double slit, however, it’s possible to perform such things as measuring the wavelength of light, measuring the speed of light, or measuring the distance between the double slit and the screen.

Make a double slit by opening the gap between two razor blades and inserting a thin strip of tungsten filament. Secure the filament using miniature watch or camera screws. You can also use small gauge wire (30 gauge or higher) or a strand of hair (human hair measures about 100 micrometers across). Measure the filament or wire with a micrometer. Next, adjust the spacing between the razor blades so the gap is less than a millimeter or so across. The filament should be positioned in the middle of the gap.

ill. 7. A double slit using a small filament (I used 30-gauge wire-wrap wire. Stretch the filament between the blades; adjust the gap between the blades so that it's even on both sides of the filament. (A) Details of the double slit. (B) arrangement of laser, single slit, and double slit for experiments to follow.

Another more accurate method is to use a Ronchi ruling, which is a precision-made optical component intended for testing the flatness (or equal curvature) of lenses, mirrors, and glass. The ruling is made by scribing lines in a piece of glass. The spacing between the lines is carefully controlled. Typical Ronchi rulings come with 50, 100, and 200 lines per inch. At 50 lines per inch, the distance between gaps is 0.02 inch, or 0.508mm.

With the distance between gaps known, you can now perform some experiments. Set up the double slit precisely 1 meter (1,000 mm) from a white or frosted glass screen. Turn on the laser, and as accurately as possible, measure the distance between fringes. With a red helium-neon laser, the distance should be approximately 1.25 mm between fringes. If this proves too difficult to measure, increase the distance to 5 meters (5,000 mm). Now you are ready to perform some calculations.

Here is the formula for computing light wavelength.

W = (f x b) / d

where w is the wavelength of the light, f is the distance between two bright fringes, b is the distance between the slits, and d is the distance between the slits and the viewing screen.

Measuring the fringes indicates they are 1.25 mm apart using a 50-line-per-inch Ronchi ruling. And you know that the distance between the slits is 0.508 mm. Multiply 1.25 times 0.508 and you get 0.635. Now divide the result by 1,000 (for the distance between slits and screen) and you get 0.000635. That is very close to the wavelength, in millimeters, of red He-Ne light.

You can interpolate the formula (using standard algebra) to find the distance between the slits and screen. The formula becomes:

d = (f x b) / w

As an example, if the fringes measure 6.25 mm apart with a slit distance of .508 mm and the wavelength of the laser light is 0.000632 mm, the distance is 5,017 mm, or a little over 5 meters.

If you aren’t sure of the spacing between slits, you can use the formula:

b = (w x d) / f

The result is the spacing, in millimeters. Calculating the space between slits is handy if you use the tungsten-and-razor-blade method. Two other (less accurate) methods of making double slits include:

* Photograph two white lines with color slide film and use the film as an aperture.

* Scribe two lines in film, electrical tape, or aluminum foil.

You might also use this technique to measure small parts like machine pins, needles, and wire. The spacing of the fringes reveals the diameter or width of the part. Keep in mind that the best diffraction effects are obtained when the slits (and center object) have the thinnest edges possible. The fringes disappear with thicker edges.

Calculating Frequency, Wavelength, and Velocity

Knowing the wavelength of the light used in the diffraction experiments can be used to calculate the frequency of the light as well as its velocity. Use the following formulas for calculating frequency, wavelength, and velocity of light:

velocity = frequency x wavelength

These figures will help you in your calculations:

* Speed of light in a vacuum: 299,792.5 km/sec

* Approximate speed of light in air: 299,705.6 km/sec (sea level, 30°C)

* He-Ne laser light: 632.8 nm

* Green line of argon laser: 514.5 nm

* Blue line of argon laser: 488.0 nm

As an example, to calculate the frequency of red He-Ne laser light, take velocity (299,792.5) divided by wavelength (632.8). The result is 473.7555 terahertz.

Using Diffraction Gratings

A diffraction grating is a piece of metal or film that has hundreds or thousands of tiny lines scribed in its surface. The grating can be either transmissive (you can see through it) or reflective (you see light bounce off of it). Although the reflective type makes interesting-looking jewelry, it has limited use in laser experiments. A small piece (1-inch square) of transmissive diffraction grating can be used for numerous experiments. The exact number of scribes isn't important for general tinkering, but one with 10,000 to 15,000 lines per inch should do nicely. Edmund Scientific and American Optical Center sell diffraction gratings and kits at reasonable cost.

The diffraction grating acts as an almost unlimited number of slits and disperses white light into its component colors. When used with laser light, a diffraction grating splits the beam and makes many sub-beams. These additional beams are the secondary wavelets that you created when experimenting with the diffraction slits detailed above. The beams are spaced far apart because the scribes in the diffraction grating are so close together.

The pattern and spacing of the beams depends on the grating. A criss-cross pattern shows a grating that has been scribed both horizontally and vertically. You can obtain the criss-cross material from special effects “rainbow” sunglasses sold by Edmund. Most gratings, particularly those used in compact disc players and scientific instruments, are scribed in one direction only. In that case, you see a single row of dots.

Besides breaking up the beam into many sub-beams, one interesting experiment is what might be called “diffraction topology.” The criss-cross rainbow glasses material shows the effect most readily. Put on the glasses and point the laser beam at a point in front of you. Tilt the glasses on your head and note that the sub-beams appear almost 3-D, as if you could reach out and grab them. Of course, they aren’t there but the illusion seems real.

Now move the beam so that it strikes objects further away and closer to you. Not only does the apparent perspective of the sub-beams change, but so does the distance between the spots. The closer the object, the greater the perspective and the closer the spots are spaced to one another. Scan the laser back and forth and the perspective and distance of spots changes in such a way that you can visually see the topology of the ground and objects in front of you.

One practical application of this effect is to focus the diffracted light from the film onto a solid-state imager or video camera, then route the signal to a computer. A program running on the computer analyzes the instantaneous arrangement of the dots and correlates it to distance. If the laser beam is scanned up and down and right and left like the electron beam in a television set, the topology of an object can be plotted. The easy part is setting up the laser, diffraction grating, and video system; the hard part is writing the computer software! Anybody want to give it a try?

While you’ve got your hands on a diffraction grating, look at the orange gas discharge coming from around the tube. You’ll be startled at all the bright, well-defined colors. Each band of light represents a wavelength created in the helium-neon mixture. The dark portions between each color represents wavelengths not produced by the gases.

If you can’t readily see the lines with the diffraction grating you’re using, you might have better luck with a home-built pocket spectroscope. Place a plastic or cardboard cap on the end of a 1-inch diameter tube. Saw or drill a slit in the cap, or make a gap using a pair of razor blades, as detailed earlier in this section. On the other end of the tube, glue on a piece of transmissive diffraction grating. Aim the slit-end of the spectroscope at the light source and view the spectra by looking at the inside of the tube, as shown in ill. 8. Don’t look directly at the slit.

ill. 8. You can construct your own pocket spectroscope with a short 6-inch long cardboard tube, slit (cutout or razor blade), and diffraction grating View the diffracted light by looking at the inside wall of the tube. Rotate the tube (and grating) to increase or decrease the width of the spectra lines.

POLARIZED LIGHT AND POLARIZING MATERIALS

When I was a kid, I learned about polarized light the same way that most other people did at the time—in ads for sunglasses. Specially made sunglasses somehow blocked glare by the magic of polarization. Not until I began experimenting with lasers did I learn the true nature of polarized light and how the sunglasses perform their tricks. Be aware that the subject of polarized light is extensive and at times complicated. The following is just a brief overview to help you understand how the experiments in this section work.

Consult a book on optics for more details. TABLE 4 indicates the materials necessary to performs the experiments in this section.

What Is Polarized Light

Light is composed of two components: a magnetic field component and an electrical field component (thus the term electromagnetic). These components, or vectors, are both waves that travel together, but at 90-degree angles. That is, if one vector travels up and down, the other travels right and left. Ill. 9 shows a diagram of the magnetic and electric field vectors traveling as waves through space.

ill. 9. A pictorial representation of the electric and magnetic components of light waves.

In sunlight, the phase of the electrical and magnetic vectors are constantly changing (but the two are 90 degrees out of phase to one another). At one moment, the phase of, say, the electric field vector might be 0 degrees; at another time it might be 38 degrees. An instant later it might be at 187 degrees. Such light is said to be unpolarized. This is the nature of light from the sun, desk lamp, flashlight, and most any other illumination source.

By locking the phase of the fields vectors or by filtering out those phases that don’t match up to the ones desired, it’s possible to polarize light. There are three general types of polarized light:

* Plane (or linearly) polarized, where the electric and magnetic vectors don't change phase.

* Circularly polarized, where the phase of the electric field vector rotates from 0 to 360 degrees in even and well-defined steps.

* Elliptically polarized, same as above but the instantaneous amplitude of the electric field vector constantly changes or isn't the same amplitude as the magnetic field vector.

The terms plane, circular, and elliptical refer to the imaginary pattern the light would make on a viewing screen. Looking at a beam of plane-polarized light head-on, it would appear as in ill. bA, with the electric field vector occupying a horizontal or vertical plane. Circularly and elliptically polarized light take on a more two-dimensional figure— either a circle or ellipse. The symmetry of the ellipse depends entirely on the instantaneous amplitude of the electric field vector. Their head-on patterns are shown in ill. 10B and b10C.

ill. 10. The “end-view” of three types of polarized light: plane, elliptical, and circular. A. Plane polarized; B. Elliptically polarized; C. Circularly polarized

Polarized light is most commonly created from unpolarized light by the use of a filter. A polarizing filter, typically made from organic or chemical dyes, blocks out those phases that don’t lie along a specific axis. As you might guess, this means that a good portion of the light won’t get through; but in practice, no polarizing filter is 100 percent efficient at absorbing off-axis phases. That means that only about 35 to 50 percent of the light is eventually blocked.

You can most easily experiment with polarized light using two polarizing filters (one is the polarizer, the other the analyzer, as shown in ill. 11). Sandwich the filters together and rotate one of them as you view a light source. The intensity of the light will increase and decrease every 90 degrees of rotation.

All lasers emit polarized light, with either of two orthogonal planes of polarization. But the-exact phase of the polarization varies over time as does the relative amplitude of the polarization components. You can repeat the experiments with the two polarizing filters with your He-Ne laser. As you rotate one of the filters, the intensity of the beam increases or decreases.

Lasers can be linearly polarized in one plane with the use of Brewster’s window placed in front of the fully reflective mirror. This window is a piece of clear glass titled at an angle (precisely 56 degrees, 39 minutes) that “absorbs” one of the planes of polarization. As a result, the output beam is plane-polarized with a purity exceeding 300:1.

ill. 12. A laser, piece of glass, and polarizer are the components you need to experiment with polarization by reflection. Watch the intensity of the beam change as you rotate the polarizer.

The Brewster’s Angle window works by polarization by reflection. You can experiment with this technique using a coated or uncoated piece of plate glass (1-inch square should do it). Position the laser, glass, and polarizing filter as shown in ill. 12. With the glass tilted at an angle of approximately 57 degrees, rotate the polarizing filter while watching the reflected (not transmitted) beam. The intensity of the beam should increase and decrease. If you don’t witness a discernible effect, alter the angle of the glass a bit and try again. A precision metal protractor can help you position the glass at the required Brewster’s Angle. Ill. 13 shows what happens to the polarization components as they reflect on contact with the glass.

ill. 13. A graphic illustration of the amount of reflectivity of the p and s planes at different angles of incidence.

Experimenting With Calcite

There are a number of polarizing materials designed for use with optics and lasers, including birefringent polarizers, Wallaston prisms, dichroic sheet polarizers, and Glan Taylor polarizers. Polarization through birefringence is an interesting effect that you can readily investigate with a dollar chunk of cakite and a polarizing filter. Calcite is a commonly occurring mineral that takes on many forms, including limestone and marble. In one form it's an optically clear rhombohedral crystal.

Although some optics-grade calcite polarizing prisms are priced in excess of $500, you can make your own (for experimental purposes) for about a dollar. Many rock stores and natural history museum gift stores sell chunks of calcite at reasonable cost. This calcite is far from optically pure, but it’s good enough for routine experiments. You can always tell a calcite crystal by looking at its shape and what it does to printed material when you place it on a page from a book. As shown in ill. 14, a calcite crystal creates two images through a process called birefringence, or double refraction.

Look for a piece that’s relatively clear and large enough so that you can work with it. A few inclusions here and there won’t hurt. If the crystal has rough edges or is bro ken into an unusable shape, you can repair it by cleaving new sides. A calcite crystal will retain its rhomboid shape even if re-cleaved. You can best cleave the crystal by using a small- bladed flat screwdriver or chisel and hammer. Use the screwdriver to chip away a small layer of the crystal to expose a new face.

You may, if you wish, finish the sides using very fine-grit (300 or higher) wet/dry sandpaper, used wet. The faces of the crystal will turn a milky white, but they can be repolished using jeweler’s rouge and a buffing wheel. Rouge is available at many hardware and glass or plastics shops; you can outfit your drill motor with a suitable buffing wheel.

Point the laser into the crystal and look at the opposite side. You’ll see two beams instead of one, as indicated in ill. 15. One ray is called the ordinary ray and the other is the extraordinary ray. Depending on the optical quality of the crystal and how well you have polished its sides, the beams should project on a wall or screen located a few inches away. The interesting thing about these two beams is that they are orthogonally polarized. That is, beam A is polarized in one direction and beam B is polarized at a 90-degree angle. You can test this by rotating the polarizing filter in front of the two beams (look at the projected beams, not the spots on the filter). As you rotate the filter, one beam will become bright as the other dims. Keep rotating and they change states.

ill. 14. Calcite exhibits birefringence, causing double images. ill. 15. A single beam entering a calcite crystal is refracted into two beams—E and O rays. The refracted beams are orthogonally polarized.

Retardation Plates

Retardation plates, typically made of very thin sheets of mica or quartz, are elements primarily used in the synthesis and analysis of light in different states of polarization. There are several types of retardation plates (also called phase shifters):

* A quarter-wave retardation plate converts linearly polarized light into circularly polarized light, and vice versa.

* A half-wave retardation plate changes the polarization plane of linearly polarized light. The angle of the plane depends on the rotation of the plate.

Both quarter- and half-wave plates find use in some types of holography, interferometry, and electro-optic modulation. They are also used in most types of audio compact disc players as one of the optical components. When coupled with a polarizing beam splitter, the quarter-wave plate prevents the returning beam, (after being reflected off the surface of the disc) from re-entering the laser diode. If this were to happen, the output of the laser would no longer be coherent. A quarter-wave plate can be similarly placed in front of a polarizing filter and laser (see ill. 16) for use in the Michelson interferometer project detailed in Section 9. The retardation plate prevents light from reflecting back into the laser and ruining the accurate measurements possible with the interferometer.

ill. 16. A quarter-wave plate, in conjunction with a polarizer, can be used to prevent a reflected beam from re-entering the laser.

MANIPULATING THE LASER BEAM

Simple and inexpensive optics are all that’s required to manipulate the diameter of the beam. You can readily focus, expand, and collimate a laser beam using just one, two, or three lenses. Here are the details. Refer to TABLE 5 for a parts list.

Focusing

Any positive lens (plano-convex, double-convex, positive meniscus) can be used to focus the beam of a laser to a small point. For best results, the lens should be no more than about 50 to 100 percent larger than the diameter of the beam, or the light won’t be focused into the smallest possible dot. To use a particular lens to focus the light from your laser, it might be necessary to first expand the beam to cover more area of the lens. Refrain from expanding the beam so that it fills the entire diameter of the lens.

Note that the beam is focused at the focal point of the lens, as illustrated in ill. 17. The size of the spot is the smallest when the viewing screen (or other media such as the surface of a compact disc) is placed at the focal length of the lens. The spot appears out of focus at any other distance.

If you don’t know the focal distance of a particular lens, you can calculate it by holding it up to a strong point source (laser, sun, etc.) and varying the distance between lens and focal plane. Measure the distance, as shown in ill. 18, when the spot is the smallest.

ill. 17. Positive lenses focus light to a point. The size of the beam increases at distances ahead or beyond this focal point.

ill. 18. Measure the focal length using the setup shown here. The ruler can be marked off in inches or centimeters, as you prefer.

Expanding

Any negative lens (plano-concave, double-concave, negative meniscus) can be used to expand the beam. An expanded beam is useful in holography, interferometry, and other applications where it's necessary to spread the thin beam of the laser into a wider area. You might also want to expand the beam to a certain diameter before focusing it with a positive lens.

The degree of beam spread depends on the focal length of the lens (remember that negative lenses have negative focal points because their focal point appears behind the lens instead of in front of it). The shorter the focal length, the greater the beam spread. If you need to cover a very wide area with the beam, you may combine two or more negative lenses. The beam is expanded each time it passes through a lens. Remember to use successively larger lenses as the beam is expanded.

ill. 19. A common optical arrangement for lasers is the beam expander/collimator, created by coupling a negative and positive lens. Note that this arrangement is modeled after the design of a simple Galilean telescope, used in reverse.

ill. 20. Beam divergence is greatly reduced over long distances by the use of an expander/collimator. This graph shows the approximate beam spread of an He-Ne laser with and without collimating optics.

Collimating

By carefully positioning the distance between the negative and positive lens, it’s possible to enlarge the beam and make its light rays parallel again. A double-concave and double-convex lens positioned as shown in ill. 19 make it a collimator, a useful device that can be used to enlarge the beam yet still maintain collimation and to reduce divergence over long distances. Ill. 20 shows a graph that compares the divergence of the beam from a He-Ne laser with and without collimating optics. Although the collimator initially makes the beam wider, it greatly decreases divergence over long distances.

In order for the beam to be collimated, the distance between lenses A and B must be equal to the focal length of the double-convex lens B. Again, if you don’t already know the focal length of this lens, determine it using a point light source and ruler. Collimation allows for the sharpest focus of the beam. Rather than simply expand the laser beam to fill the focusing lens, first expand and collimate it.

A small telescope (such as a spotting scope or rifle scope) makes a good laser beam collimator. Just reverse the scope so that the beam enters the objective and exits the eyepiece. An inexpensive ($10) sports scope can be used as an excellent collimating telescope. Mount the scope in front of the laser using clamps or brackets. Adjust for the smallest divergence by focusing the scope.