Purpose

To study basic properties of light and its interaction with matter using a laser.

Equipment

Helium-Neon Laser, diffraction grating, prism, glass plate, polarizer, an assortment of 5 mounted slits, protractor, stand for slits, meter stick, ruler.

WARNING: Never look directly into the laser or its specular reflection!

Preliminary Discussion

I. Lasers

An atom can absorb a photon by raising an electron from the ground state to an excited state. A short time later, spontaneous emission takes place, and the excited atom returns to its ground state by emitting a photon which has energy equal to the energy level difference between the excited and ground states. The direction and phase of these spontaneously emitted photons are completely random, which renders them useless if one wants a directed beam of light.

Albert Einstein proposed an idea he called stimulated emission of radiation, which is the basis for all laser light emission (laser is the acronym for Light Amplification by Stimulated Emission of Radiation). He reasoned that if a photon with the same frequency as the spontaneously emitted photon scattered from an atom that was in its excited state, the atom could release a photon identical to the first in frequency, direction, phase and polarization. The two photons are thus, coherent.

The atoms inside a laser tube have to be brought to the necessary excited state independently of the photons. This process of raising atoms to a higher energy level is known as "pumping". Lasers can be pumped in several different ways. The helium-neon lasers you will use, work by applying a high voltage across the laser tube. This causes the helium inside the tube to absorb energy. After gaining energy, a helium atom eventually collides with a neon atom which absorbs the energy that was contained in the helium atom. The neon atom then spontaneously emits a photon which produces red light. This light corresponds to the strongest and most visible of the wavelengths of light your helium-neon laser emits.

For a continuously emitting laser, though, a majority of the atoms must be pumped to an excited state, that is, there must be a population inversion. This characteristic is maintained by pumping atoms at the same rate energy is lost. Also, two mirrors are used to amplify the beam. One mirror is almost totally reflective while the other is about 99% reflective. These mirrors are placed at opposite ends of the laser tube. This is done so that the photons emitted along the axis of the tube can then reflect back and forth through it, so that they may have a much higher chance of colliding with an excited atom than light traveling in other directions. This increases the number of photons stimulated along the axis of the tube on each pass. About 1% of the light passes the aperture on each reflection and forms the coherent laser beam.

Laser light is highly directional, monochromatic and very bright. It is directional because only the light traveling parallel to the long axis of the laser tube is amplified by stimulated emission, multiple times. The monochromaticity of a helium-neon laser emission occurs because of the single transition energy yielding visible photons. The high intensity is due to the large number of sources emitting in coherence.

II. Light - Wave Nature of Light

A. Reflection and refraction


Snell's Law, n₁sin q₁ = n₂sin q₂, relates the index of refraction of one medium, the angle of incidence of light from that medium and the index of refraction of the other medium, and the angle of refraction in that medium. A consequence of Snell's Law is that if n₁ > n₂ then q₁ < q₂. This is fine for small angles, but for some angle of incidence q₁, the angle of refraction q₂ will be 90°. At the critical angle q_c = q₁ a so-called "evanescent" wave can travel along the interface. For incident angles larger than q_c the light is totally internally reflected, no light passes through the interface.


B. Interference and diffraction


For two sources of coherent light separated by distance d (as sketched in Figure 8.1), light will destructively or constructively interfere on a screen placed far from the source. Light constructively interferes where the distance from one source to the screen is different from the distance of the other source to the screen by an integral number of wavelengths of the light illuminating the sources. That is, the path length difference for the two beams equals ml, where m is an integer (0, 1, 2, ... ) and l is the light wavelength. For destructive interference, this path length difference must be (m+½)l, the light is out of phase. As is seen in Figure 8.1, the path length difference is d sin q, where q is the angle to the position of interest on the screen.


For a single slit of width D, light from the edges of the slit can interfere with light from the center of the slit, either destructively or constructively. This is called single slit diffraction. The condition for a minimum in intensity (a dark fringe) is D sin q = ml. If there are two or more slits, you can observe the single slit diffraction pattern superimposed on the multiple slit interference pattern. Typically D the width of slits is much less than d the spacing between slits, so the single slit diffraction pattern is broader than the multiple slit interference pattern.


Diffraction gratings have thousands of lines per inch patterned onto a film. The gap between each line acts as a source. The same multiple slit interference formula applies as described above, with d the distance between lines.


C. Polarization


Light is a transverse electromagnetic wave, and both its electric and magnetic field amplitudes oscillate perpendicular to its direction of travel.  Consider the electric field vector of a plane wave propagating in the x direction E(x,t) = E_osin(kx- t). The orientation of E_o is always in the yz plane. If a beam of light is composed of electric field vectors with a uniform distribution in the yz plane, it is unpolarized.  If one direction for E_o is favored the light is partially polarized. Tools have been made which can isolate one polarization from another.

III. Experimental Work

A.  Refraction and Reflection


Place the empty rectangular container in the path of the laser such that the light hits the glass at an angle of incidence of about 30°.  Slide a piece of paper under the container.  Trace around the container and mark where the laser beam enters and leaves.  Fill the container with water.  Again, find where the beam leaves the glass and mark that point on your paper.  Find the next three points about the edge where the laser leaves the container.  Remove the container.


On the paper, trace the first line of each of the two paths you made.  (One path made through air, one through water.)  Why are the paths different?  Draw tangents to the points you found where the laser leaves the container.  Trace the path of the beam as it went through the water.  Measure the angles of incidence, reflection, and refraction for the first three points.  From your data, and using Snell's Law, find the index of refraction of the water (You can ignore the glass).


Put the full container on another piece of paper. Swish a bar of soap in the water once or twice to yield more scattering from the solution. Look at the scattering from above, from the side, and at a small angle from in front of the beam. In which direction is the scattered intensity highest? Look at the scattered light from above and from the side through a polarizer. Is the polarization different? Move the containerso that the beam enters almost tangent to the container. Can you see when the beam becomes totally internally reflecting? Since this occurs only when going from higher index of refraction to lower, the internal reflection must be occurring at the glass-air interface. How many reflected beams can you see in the solution?


B. Determine the wavelength of the light.


The slits you have been provided with may be used to determine the wavelength of light, by measuring the interference pattern of the light diffracted from them. You should shine the laser beam through the slits onto the wall opposite your bench. Calculate the wavelength of the laser for each slit arrangement and average your results to obtain a best guess for the wavelength.


The configuration of each slit set is shown schematically in Figure 8.2.


Using double slits, find the wavelength of the laser using d sin q = ml, where d is the distance between slit centers, q is the angle to the m^th maximum and l is the wavelength of the laser (see figure 1). You can measure the angle q by measuring the distance L from the slit to the central spot of the laser on the wall, and measuring the distance y perpendicular to the beam, from the central spot to the m^th maximum. Then tan q = y/L.


Find the wavelength again, using a single slit and the formula D sin q = ml, where D is the slit width and q is the angle from the slit to the first minimum in intensity.


Again find the wavelength using multiple slits. Use the same formula as for double slits. Can you see any difference in the characteristics of the diffraction pattern for multiple slits as compared with single or double slits?


The diffraction grating is essentially many slits. It looks almost transparent but if you look through it at white light, you may be able to see a rainbow of colors (why?). Put the diffraction grating in your slit mount. Note that the diffraction spots are at much larger angles. By using the multiple slit formula, calculate the spacing between slits on the grating, and the inverse, the number of slits per centimeter. You may use either your experimentally determined wavelength, or the wavelength provided by your instructor.


C. Determination of the index of refraction.


Using your measurement of l, find the index of refraction of the glass provided. You can do this by measuring the spacing between adjacent reflected spots, as shown in Figure 8.3. Place a protractor on the board with the zero - 180° line directly below the beam. Stand the rectangular glass plate on a long edge on top of the protractor with the side nearest the laser above the center point of the protractor. The opposite end of the glass plate should be above an angle marking. This allows you to measure q. Measure the separation between adjacent reflected rays a, for an angle of incidence q larger than 60°, which results in a reasonably large separation a. The refractive index is then given by


.


D. Polarization Effects


Direct the laser beam at a wall. Observe the variation in intensity as you rotate a polarizer in the beam. What does that imply about the polarization of the laser?  Place another polarizer between the first polarizer and the screen.  Rotate it until the beam is extinguished.  (It is easier to place the one polarizer in the aperture of the laser and hold the other near the wall.)  Put another polarizer between the first and third polarizers.  Rotate it through 360°.  For what orientations is the beam transmitted?  How is it possible that inserting a third polarizer can allow light to be transmitted?