An Untitled Derivation of the Law of Refraction, December 1681

Abstract
Let AC be a ray coming from the medium DC into the medium CE, and let the density of the former to the latter be as d to e. It is asked, how should the ray ACB be directed so that it is the easiest path of all, or that (AC x d) + (CB x e) is a minimum. Let DC = l, and EC = m. It is given also that FG = f, and let AD = FC = x, CG = EB = f – x. Therefore, AC = √(l2 + x2) and CB = √(m2 + f2 +x2 – 2fx). 2 It will then be the case that d√(l2 + x2) + e√(m2 + f2 + x2 – 2fx is equal to a minimum. Therefore, through my method of tangents it is the case that: (2dx/(√(l2 +x2)(AC))) + ((2ex -2ef)/ (√(m2 +f2 +x2 +2fx)(BC))) = 0. That is, it will be the case that AC/BC = dx/e(f-x). Now if we suppose that AC and BC are equal, it will be the case that f – x is to x, as d to e. Therefore, if a circle, with its center at C, is described by the ray CA or CB, AD or “x,” – the sine of the angle of incidence – will be to BE or “f – x,” – the sine of the angle of refraction – as e, the density of the medium of refraction, will be to d, the density of the medium of incidence, that is, the sines of the angles will be in reciprocal relation to the mediums or densities.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 10,941
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA

No citations found.

Similar books and articles
John Dilworth (2003). Medium, Subject Matter and Representation. Southern Journal of Philosophy 41 (1):45-62.
Max Albert (2002). Resolving Neyman's Paradox. British Journal for the Philosophy of Science 53 (1):69-76.
André Kukla (1994). Medium AI and Experimental Science. Philosophical Psychology 7 (4):493-5012.
Analytics

Monthly downloads

Added to index

2010-12-22

Total downloads

9 ( #156,823 of 1,100,758 )

Recent downloads (6 months)

1 ( #289,565 of 1,100,758 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.