MadSci Net: Physics (View this file without Frames) |
Greetings: The references for my answers are the following: 1. Julie Schnapf, "How Photoreceptors Respond to Light", Scientific American, April 1987 2. S. Hecht, S. Schlaer and M.H. Pirenne, "Energy, Quanta and vision." Journal of the Optical Society of America, 38, 196-208 (1942) 3. E. L. Dereniak, D. G. Crowe, " Optical Radiation Detectors",John Wiley and Sons, 1984. Vision begins when electromagnetic energy packets called photons are converted by the rods and cones in the eye’s retina into neural signals for transmission to the brain. The eye can sense light from red wavelengths from 720 nanometers (28.3 microinches) to 400 nm (15.7 microinches) violet wavelengths. The most sensitive wavelength for rods is 520 nm, and for cones 560 nm, both wavelengths are in the green portion of the spectrum. For the dark adapted eye the rods are about 10,000 times more sensitive than the color sensing cones. Because lasers can generate light at a single wavelength we can use the more familiar standard physical units of measurement rather than photometry and illumination units which must be used for white light sources that generate the entire color spectrum that the human eye can sense. When you ask about seeing the laser beam I assume you mean directly from the laser into the eye. Seeing a beam from the side depends on dust and particles to scatter light out of the beam into the eye and this becomes a complex calculation and knowledge of the particle size distribution and particle density in the air is required. In very clear air or in a vacuum you cannot see a laser beam from the side. I use the particles in an air freshener aerosol spray to make laser beams visible from the side in class room demonstrations. Laboratory measurements on rods have indicated that each rod can be stimulated by a single photon; however, the human eye requires that about 10 rods must be stimulated in about one tenth of a second before the brain can detect the presence of light reliably (Reference 2). About 90 % of the photons entering the eye are absorbed before reaching the retina so about 1000 green photons must enter the iris each second to have 100 photons excite the dark adapted rods to produce vision in the brain.Measurements show that the dark adapted eye has only a few percent of the maximum green responce in the red wavelengths near 632nm while the cones have about 50% of the maximum green responce at 632nm. Thus the eye would be most sensitive to green lasers; however,lasers used in most low cost applications are red lasers operating at 632 nm. If we assume that the laser is a red Helium Neon gas laser or a red laser diode pointer operating at 632 nm, the type laser used in bar code readers in supermarket check out stands, the photon energy is Planck’s constant ( 6.625 times 10 to the power - 34 ) times the laser frequency (475 TeraHz , 475 thousand million cycles per second) equals 3.14 times 10 to the power - 19 watts (Joule/second). Working backwards to answer you question, we need about 10 thousand red photons per second to enter the eye and pass through the iris or 3.14 times 10 to the power -15 watts (.000,000,000,000,003,14 watts) a very, very small power! The dark adapted iris is about 8 millimeters (0.3 inches) in diameter with an area of 0.5 square centimeters (.09 square inches). The power density incident on the eye to excite vision must then be 6.28 times 10 to the power -15 watts per square centimeter to get the 10,000 photons into the iris. For a reference, laser safety limits for the eye require power densities less than one hundred microwatts (.0001 watt) per square centimeter. Using the above numbers, if you were to take a small red laser pointer with one milliwatt of output power exiting the laser in a collimated (parallel) one millimeter diameter beam, the beam would diverge (spread out) in about a one milliradian angle (.06 degrees). In very clear air you calculations show that you should be able to see this beam with your eyes at a distance of 5 kilometers (3.1 miles). A green laser should be visible 10 times farther! I have actually seen a one milliwatt red laser 32 km (20 miles) away across Santa Monica Bay from our laboratory as a very bright red light indicating to me that the photo absorption in the eye may be less that that reported in the references and the bright red color indicates that the cones were also responding to the laser beam. The experiments in the references did not use coherent laser light and that may also be a factor in determining the eye's sensitivity. CAUTION: Never look directly into a laser beam when close to the laser. This includes low power laser pointers. The power density of the beam must be reduced to safe levels for direct viewing! Best regards, your Mad Scientist Adrian Popa
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