EXAMPLE: Intensity of a flashlight

ECE532 Biomedical Optics ©1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute

A cheap flashlight projects a beam that is 200 mW to create a 10-cm-diameter spot on a wall 25 cm meters away. The face of the flashlight has a 3-cm diameter. What is the radiant intensity of beam?

• The geometry of the problem is:
  
• The diameter of the spot on the wall is 10 cm. The diameter of the face of the flashlight is 3 cm. The apparent source of the flashlight is located at a virtual position x [cm] behind the lamp and parabolic reflector of the flashlight. The value of x is solved and equals 10.7 cm:
  
  
  
• The distance from virtual position of source to wall is R = 25 + 10.7 = 35.7 cm. A sphere with radius R would have a total surface area of A_sphere = 4(35.7 cm)² = 16016 cm².
• The circular area of the spot on the wall is A_spot = (5 cm)² = 78.5 cm².
• The solid angle of the cone of light radiating from the flashlight equal (4 [sr]) A_spot/A_sphere:
  
  
• The radiant intensity is P/: