Refraction

Discussion

introduction

Willebrord Snel (1580–1626) Netherlands. "Although he discovered the law of refraction, a basis of modern geometric optics, in 1621, he did not publish it and only in 1703 did it become known when Huygens published Snell's law in Dioptrica." Snell also studied navigation and proposed the method of triangulation, which is the foundation of geodesy (the branch of mathematics dealing with the measurement of features on the earth). For some reason, the law named after the man is spelled incorrectly. Snel the man vs. Snell the law.

sin θi  = constant
sin θr

and then

n1 sin θ1 = n2 sin θ2

"This form of Snell's law was actually published by René Descartes (1596–1650) France in La Dioptrique (1637). Snell did discover the relationship but articulated it in a different way. Today it is the form used by Descartes that is called Snell's law."

The index of refraction.

n =  c
v

where

n =  index of refraction
c =  speed of light in a vacuum
v =  speed of light in a medium

The index of refraction is somewhat related to density, as one would expect. This graph is for transparent minerals. Someone should make one for liquids and see what happens.

[slide]

material index   material index
acetone 1.36   helium (gas) 1.000036
air (–15 ℃) 1.00030942   helium (liquid) ??
air ( 0 ℃) 1.00029238   hydrogen (gas) 1.000140
air (+15 ℃) 1.00027712   hydrogen (liquid) 1.0974
air (+30 ℃) 1.00026337   lucite 1.495
air (+60 ℃) 1.00023958   milk 1.35
alcohol, ethyl (grain) 1.361   oil, microscope 1.515
alcohol, methyl (wood) 1.328   oil, vegetable (50 ℃) 1.47
amber 1.546   opticon (epoxy) 1.545
amethyst 1.544   perovskite 2.38
benzene 1.501   plexiglas 1.488
butter (40 ℃) 1.455   quartz, crystalline 1.544
butter (60 ℃) 1.447   quartz, fused silica 1.4585
calcite 1.486   ruby 1.76
cd/dvd 1.55   salt 1.516
cocoa butter (40 ℃) 1.457   sapphire 1.76
diamond 2.418   sphalerite 2.428
eglestonite 2.49   topaz 1.62
emerald 1.576   turpentine 1.472
emerald, synth flux 1.561   ulexite 1.49
emerald, synth hydro 1.568   vacuum 1 exactly
eye, cornea 1.38   water (ice) 1.309
eye, aqueous humor 1.33   water (liquid, 0 ℃) 1.33346
eye, lens cover 1.38   water (liquid, 20 ℃) 1.33283
eye, lens 1.41   water (liquid, 100 ℃) 1.31766
eye, vitreous humor 1.34   water (vapor) 1.000261
fluorite 1.387   zircon, high 1.960
franklinite 2.36   zircon, low 1.920
glass, borosilicate (pyrex) 1.474   zirconia, cubic 2.173
glass, crown (soda-lime) 1.512      
glass, fiber 1.560      
glass, flint (29% lead) 1.569      
glass, flint (55% lead) 1.669      
glass, flint (71% lead) 1.805      
glass, fused silica 1.4585      
glycerin 1.473      
Index of refraction for selected materials (λ ~ 590 nm)

apparent depth

Don't go in the water.