Hold the light source directly against a piece of paper. Measure the diameter of the beam as it passes through the paper. Record the result as the original beam diameter.
Place the light source on a flat, steady surface. Erect a sheet of white paper (or black if using a white beam) a known distance away from the light source.
Measure the diameter of the beam as it hits the paper. Record the result on the sheet as the diameter.
Move the piece of paper farther away from the light at regular intervals. Record the new diameter on the sheet at each location.
Find the increase in beam diameter by subtracting the original beam diameter from the diameter on the sheet. Repeat for all data points you recorded. For example, if the beam has a width of 1 mm and appears 3 mm at 1 foot, 6 mm at 2 feet and 9 mm at 3 feet, then the increase in beam diameter is 2 mm (3 - 1) at 1 foot, 5 mm (6 - 1) at 2 feet and 8 mm (9 - 1) at 3 feet.
Divide the increase in beam diameter by the distance from the sheet for all data points. Record the result for each point. Average the results for all points to determine the angle of divergence in radians. For example: 3 mm divided by 1 foot equals 3 radians, 5 mm divided by 2 feet equals 2.5 radians and 8 mm divided by 3 feet equals 2.666 radians.