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shareRefraction
Discussion
introduction
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Willebrord van Roijen Snell (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 result 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).
| 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 | is the index of refraction |
| c | is the speed of light in vacuum |
| v | is the 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.
[magnify]
| Index of Refraction for Selected Materials (λ ~ 590 nm) | ||||
| 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 | 1.45843 | |
| 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, flint (29% lead) | 1.569 | |||
| glass, flint (55% lead) | 1.669 | |||
| glass, flint (71% lead) | 1.805 | |||
| glass, fused silica | 1.459 | |||
| glycerin | 1.473 | |||
apparent depth
Don't go in the water.
total internal reflection
light traveling from a slow medium to a fast medium
critical angle
| n1 sin θ1 | = | n2 sin θ2 | |||
| n1 sin θc | = | n2 sin 90° | |||
| sin θc | = | n2 | in general | ||
| n1 | |||||
| sin θc | = | 1 | when the second media is air | ||
| n1 | |||||
inferior mirage
An inferior mirage.
It is sometimes possible to see over the horizon. The superior mirage or Fata Morgana.
Fata Morgana (superior mirage), the Italian name of the enchanted, half sister of King Arthur. Italian writers and poets described these effects as seen over the straights of Messina, between Italy and Sicily. Although the effects occur worldwide, the Italian name sticks. (From Greenler's book?)
Quote from somebody
Under highly stable atmospheric conditions (typically on calm, clear nights), the radar beam can be refracted almost directly into the ground at some distance from the radar, resulting in an area of intense-looking echoes. This "anomalous propagation" phenomenon (commonly known as AP) is much less common than ground clutter. Certain sites situated at low elevations on coastlines regularly detect "sea return", a phenomenon similar to ground clutter except that the echoes come from ocean waves.
dispersion
rainbow
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| A double rainbow seen on a depressingly gray day in Clinton, Missouri. | You don't need rain for a rainbow. This picture was taken at Niagara Falls, New York. |
halo
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| A simple halo around a church in Milwaukee, Wisconsin. | A 22° halo with an upper tangent arc and two sun dogs as seen in New York City. The sun is blocked by the author's bicycle gloved fist. |
Dispersion is generally highest in solids and lowest in gases.
Dispersion is often measured in terms of the coefficient of dispersion, which is defined as the difference between the refractive indices for for two prominent lines in the spectrum of hydrogen — the blue F line at 486.1 nm and the red C line at 656.3 nm.
nf − nc
Another common measure of dispersion is the dispersive power.
| nf − nc |
| nD − 1 |
where nD is the index of refraction for the yellow D line of sodium at 589.0 nm.
Use of a single number to quantify dispersion is rather misleading. Index and wavelength are not linearly related. Dispersion is best quantified as the rate of change of index of refraction with wavelength.
| dn |
| dλ |
For most transparent materials, a graph of index versus wavelength is curve with a few general characteristics.
- The index of refraction is larger for shorter wavelengths; thus, its slope is always negative.
- Dispersion (the rate of change of index with wavelength) is greater for shorter wavelengths; thus, the graph starts out steep and gradually levels off.
birefringence
Calcite is a common, transparent mineral. It can be found throughout the world, but some of the best samples were originally found in Iceland. Pieces of this mineral are easily split (or cleaved as the geologists say) into parallelogram-faced prismatic chunks. Nonmetallic minerals that cleave easily were called spar in German and so calcite is sometimes also known as Iceland spar. It is of little economic importance by itself (although it is a component of limestone, which is used to make cement), but is of some scientific importance. It has been known for several centuries that light transmitted through calcite takes two paths. This can best be seen by laying a large crystal of it on a page of text. Every letter can be seen twice. This phenomena is known as double refraction or birefringence.
Double Refraction Through a Piece of Calcite
A ray of light incident on a doubly refractive or birefringent material divides into two rays: an ordinary ray (or o ray or ω [omega] ray) and an extraordinary ray (or e ray or ε [epsilon] ray). As the name implies, the o ray behaves in an "ordinary" way, following Snell's law without a problem. The ratio of the sine of the angle of incidence to the sine of the angle of ordinary refraction is a constant. The e ray gets its name because it does not obey this rule.
falls apart here …
Birefringence is only a property of solids
When the incident angle is just right, the o and e rays will follow the same path and the birefringence cannot be seen geometrically. At all other angles, the the two rays will follow different paths. Thus, the index of refraction for extraordinary rays is also a continuous function of direction. The index of refraction for the ordinary ray is constant and is independent of direction
The index of refraction for the extraordinary ray is a continuous function of direction. The index of refraction for the ordinary ray is independent of direction. The two indices of refraction are equal only in the direction of an optic axis.
The measure of birefringence (δ [delta]) is the difference between the indices of refraction of the two rays.
δ = ne − no
In some materials (like calcite) ne < no and the birefringence is less than zero (that is, the e ray is refracted less than the o ray) and the material is said to be optically negative. In other materials (like quartz) the reverse is true and these materials are said to be optically positive. Materials that do not show birefringence are said to be isotropic (like diamond); that is, they behave the same no mater what the alignment of the crystal is relative to the incident ray.
| Types of Refraction | |||
| optical behavior | comment | examples | |
|---|---|---|---|
| isotropic (linear) | |
single refraction | gases, liquids, glasses, diamond |
| uniaxial negative | |
double refraction e ray travels faster |
calcite, tourmaline, sodium nitrate |
| uniaxial positive | |
double refraction o ray travels faster |
ice, quartz, rutile |
| biaxial | |
triple refraction | mica, perovskite, topaz |
| Index of Refefraction for Selected Nonlinear Minerals (λ ~ 590 nm) | ||||
| uniaxial minerals | no | ne | δ | |
|---|---|---|---|---|
| beryl | Be3Al2(Si6O18) | 1.602 | 1.557 | -0.045 |
| calcite | CaCO3 | 1.658 | 1.486 | −0.172 |
| calomel | Hg2Cl2 | 1.973 | 2.656 | +0.683 |
| cinnabar | HgS | 2.905 | 3.256 | +0.351 |
| hematite | Fe2O3 | 2.940 | 3.220 | +0.287 |
| ice | H2O | 1.309 | 1.313 | +0.014 |
| lithium niobate | LiNbO3 | 2.272 | 2.187 | −0.085 |
| magnesium fluoride | MgF2 | 1.380 | 1.385 | +0.006 |
| quartz | SiO2 | 1.544 | 1.553 | +0.009 |
| ruby | Al 2O3 | 1.770 | 1.762 | −0.008 |
| rutile | TiO2 | 2.616 | 2.903 | +0.287 |
| peridot | 1.690 | 1.654 | −0.036 | |
| sapphire | Al2O3 | 1.768 | 1.760 | −0.008 |
| sodium nitrate | NaNO3 | 1.587 | 1.336 | −0.251 |
| tourmaline | 1.669 | 1.638 | −0.031 | |
| zircon, high | ZrSiO4 | 1.960 | 2.015 | +0.055 |
| zircon, low | ZrSiO4 | 1.920 | 1.967 | +0.047 |
| biaxial minerals | α | β | γ | |
| borax | 1.447 | 1.469 | 1.472 | |
| epsom salt | MgSO4·7(H2O) | 1.433 | 1.455 | 1.461 |
| mica, biotite | 1.595 | 1.640 | 1.640 | |
| mica, muscovite | 1.563 | 1.596 | 1.601 | |
| olivine | (Mg,Fe)2SiO | 1.640 | 1.660 | 1.680 |
| perovskite | CaTiO3 | 2.300 | 2.340 | 2.380 |
| topaz | 1.618 | 1.620 | 1.627 | |
| ulexite | 1.490 | 1.510 | 1.520 | |