PHO 101 Photonics Concepts
Three Rivers Community College ONLINE
Home Lab #11
YOU WILL NEED: Laser, ruler or meter sitck
Background: One feature of a laser is that the beam stays narrow over a long distance. The beam divergence is an important parameter used to describe a laser beam. If the diameter of the beam is measured at two different locations along the beam separated by a distance "L", the full angle divergence may be approximated by
The geometry of the measurement is shown in the figure below.
The formula above gives an angle measurement in radians. Most lasers have divergence in milliradians.
Many lasers have beams that are round and the divergence is the same in all directions. The beams from laser pointers usually have a rectangular cross section. In fact, laser pointers have a lens to "correct" the beam shape; without the lens the beam would be very highly elliptical, and it would have a large divergence angle (which makes it not very useful as a pointer). The correcting lens makes the beam more circular, but it is still larger in one dimension than the other.
The reason for the large divergence of the laser pointer is that a tiny diode is used to create the light. As you know, diffraction effects are greater if light passes through a small hole than through a large hole. In fact, the aperture that the light exits from is rectangular, so the light exiting from the small dimension diverges more than light exiting from the large dimension.
PROCEDURE
1. Shine the beam at a piece of paper a few feet from the laser. Measure the width of the beam in both the x and y directions. These dimensions are called "d" in the picture above, but x and y in the table. Record in the data table.
2. Without moving the laser, move the paper across the room and measure the width of the beam in both directions again. Measure also the distance between the two locations of the paper (L in the drawing above) and record in the top row of column 3 where indicated.
3. Calculate the beam divergence in both the x and y directions from the equation above.
Near Laser |
_______meters from first measurement |
Calculated Divergence (mrad) |
|
x (width of beam spot) |
|||
y (height of beam spot) |
QUESTIONS
1. Was the divergence the same or different in the x and y directions?
2. The small divergence of a laser means that the beam energy is very concentrated. The density of light energy in Watts per square meter is called the irradiance of the beam.
a. Estimate the irradiance of the laser at the farthest distance you measured. (When the paper was across the room.) The cross sectional area of the beam can be estimated from your two measurements of the beam width in part 2) of the procedure (x an y). If the x and y measurements are the same, assume the spot is a circle (A=pr2). If the measurements are different, assume the spot is a rectangle (A=lw).b. Estimate the power of your laser. (It would be better to use a power meter for this, but an estimate will prove the point just as well.) Your pointer is probably a class 3a laser, so assume P = 4 mW.
c. Calculate the irradiance = P/A
d. Now calculate the irradiance of a 60 Watt light bulb at the same distance as the farthest measurement (when the paper was across the room) . A light bulb sends its energy out over a sphere - it has a divergence angle of 360o! The light energy illuminates a sphere whose area is 4¹ r2. The irradiance at a distance r is given by
E =60 watts / 4 ¹ r2.
Compare the bulb's irradiance to that of the laser at the same distance. What is the implication for laser safety?