Message-ID: <[EMAIL PROTECTED]> Date: Sun, 13 Sep 1998 11:38:25 -0400 From: Ross McCluney <[EMAIL PROTECTED]> Organization: Florida Solar Energy Center X-Mailer: Mozilla 4.04 [en] (Win95; I) MIME-Version: 1.0 To: [EMAIL PROTECTED] Subject: Re: The Underwater Sundial Project References: <[EMAIL PROTECTED]> Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit William J. Daciuk wrote: > how would one have > to modify the hour line equation for horizontal dials to take into > account the way the refraction of water? From what I recall from high > school physics, would there not also be portions of the dial on either > side of the style where sunlight would not penetrate, due to the light > rays bouncing back off the water after a certain slant had been reached? Great idea, though how practical I'm not sure. The refractive index of water is around 1.33 for seawater. Snell's equation for the refraction of light rays through a discontinuous interface between two media, given Aair being the angle of incidence, measured from the normal (perpendicular) to the water surface and Ah2o being the angle of refraction inside the water, is given by 1.0 sin Aair = 1.33 sin Ah2o You can solve for Ah2o for rays incident from the outside and for Aair for rays reflected from the sundial and incident upon the interface from inside the water. Rays entering the water will be bent by the indicated equation, toward the normal going into a medium of higher refractive index. The degree of bending depends upon the angle of incidence, so you would have to write a computer program to calculate the coordinates of a ray from the sun at, say, 10:00 AM solar time on a given day passing through the tip of a gnomon and onto the shadow receiving surface. This could be repeated for each day of the year and for each hour mark to create a sequence of connect-the-dots patterns to mark the underwater sundial. Total internal reflection occurs only for rays incident upon the interface from within the water at an angle of incidence greater than the critical angle, the angle Ah2o for which Aair = 90 deg in the above equation. Ah2ocrit = angle whose sine is 1/1.33 in this case. This means that you could see the dial from any direction in air, but that rays reaching your eye from the sundial below the water would come from angles of incidence less than Ah2ocrit in the water, normally only of academic interest. I hope this is correct and helpful. Improved ways of putting it and corrections will be welcome. -- Ross McCluney, Ph.D. Principal Research Scientist Florida Solar Energy Center, 1679 Clearlake Rd., Cocoa, FL 32922-5703 Voice: 407-638-1414 Fax: 407-638-1439 e-mail: [EMAIL PROTECTED] Florida Solar Energy Center: http://www.fsec.ucf.edu Sundials: http://www.sunpath-designs.com Introduction to Radiometry and Photometry: http://www.artech-house.com --------------------------------------------------------------
