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[[File:Sellmeier-equation.svg|thumb|right|Refractive index vs. wavelength for [[BK7 glass]], showing measured points (blue crosses) and the Sellmeier equation (red line).]]
It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br><br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you have any type of inquiries regarding where and exactly how to utilize [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC], you can contact us at the website.
The '''Sellmeier equation''' is an [[empirical relationship]] between [[refractive index]]  and [[wavelength]] for a particular [[transparency (optics)|transparent]] [[optical medium|medium]]. The equation is used to determine the [[dispersion (optics)|dispersion]] of [[light]] in the medium.
 
It was first proposed in 1871 by Wilhelm Sellmeier, and was a development of the work of [[Augustin Louis Cauchy|Augustin Cauchy]] on [[Cauchy's equation]] for modelling dispersion.
 
==The equation==
The usual form of the equation for glasses is
 
:<math>
n^2(\lambda) = 1
+ \frac{B_1 \lambda^2 }{ \lambda^2 - C_1}
+ \frac{B_2 \lambda^2 }{ \lambda^2 - C_2}
+ \frac{B_3 \lambda^2 }{ \lambda^2 - C_3},
</math>
 
where ''n'' is the refractive index, ''λ'' is the wavelength, and ''B''<sub>1,2,3</sub> and ''C''<sub>1,2,3</sub> are experimentally determined ''Sellmeier [[coefficient]]s''.<ref>[http://www.us.schott.com/advanced_optics/english/download/schott_tie-29_refractive_index_v3_jan_2007_us.pdf Refractive index and dispersion]. Schott technical information document TIE-29 (2007).</ref> These coefficients are usually quoted for λ in [[micrometre]]s. Note that this λ is the vacuum wavelength, not that in the material itself, which is λ/''n''(λ). A different form of the equation is sometimes used for certain types of materials, e.g. [[crystal]]s.
 
As an example, the coefficients for a common [[borosilicate glass|borosilicate]] [[Crown glass (optics)|crown glass]] known as ''BK7'' are shown below:
{| class="wikitable"
|-
! Coefficient !! Value
|-
| B<sub>1</sub> || 1.03961212
|-
| B<sub>2</sub> || 0.231792344
|-
| B<sub>3</sub> || 1.01046945
|-
| C<sub>1</sub> || 6.00069867×10<sup>&minus;3</sup> μm<sup>2</sup>
|-
| C<sub>2</sub> || 2.00179144×10<sup>&minus;2</sup> μm<sup>2</sup>
|-
| C<sub>3</sub> || 1.03560653×10<sup>2</sup> μm<sup>2</sup>
|}
 
The Sellmeier coefficients for many common optical materials can be found in the online database of [http://refractiveindex.info RefractiveIndex.info].
 
For common optical glasses, the refractive index calculated with the three-term Sellmeier equation deviates from the actual refractive index by less than 5×10<sup>−6</sup> over the wavelengths range<ref>http://oharacorp.com/o2.html</ref> of 365&nbsp;nm to 2.3&nbsp;µm, which is of the order of the homogeneity of a glass sample.<ref>http://oharacorp.com/o7.html</ref> Additional terms are sometimes added to make the calculation even more precise. In its most general form, the Sellmeier equation is given as
:<math>
n^2(\lambda) = 1 + \sum_i \frac{B_i \lambda^2}{\lambda^2 - C_i},
</math>
with each term of the sum representing an [[absorption (optics)|absorption]] resonance of strength ''B''<sub>i</sub> at a wavelength √''C''<sub>i</sub>. For example, the coefficients for BK7 above correspond to two absorption resonances in the [[ultraviolet]], and one in the mid-[[infrared]] region. Close to each absorption peak, the equation gives non-physical values of ''<math>n^2</math>''=±∞, and in these wavelength regions a more precise model of dispersion such as [[Helmholtz dispersion|Helmholtz's]] must be used.
 
If all terms are specified for a material, at long wavelengths far from the absorption peaks the value of ''n'' tends to
:<math>\begin{matrix}
n \approx \sqrt{1 + \sum_i  B_i } \approx \sqrt{\varepsilon_r}
\end{matrix},</math>
where ε<sub>r</sub> is the relative [[dielectric constant]] of the medium.
 
The Sellmeier equation can also be given in another form:
:<math>
n^2(\lambda) = A + \frac{B_1}{\lambda^2 - C_1} + \frac{ B_2 \lambda^2}{\lambda^2 - C_2}.
</math>
Here the coefficient ''A'' is an approximation of the short-wavelength (e.g., ultraviolet) absorption contributions to the refractive index at longer wavelengths. Other variants of the Sellmeier equation exist that can account for a material's refractive index change due to [[temperature]], [[pressure]], and other parameters.
 
==Coefficients==
{| class="wikitable" style="text-align:center"
|+ Table of coefficients of Sellmeier equation<ref>http://cvimellesgriot.com/products/Documents/Catalog/Dispersion_Equations.pdf</ref>
|-
!Material||B<sub>1||B<sub>2||B<sub>3||C<sub>1||C<sub>2||C<sub>3
|-
|[[borosilicate glass|borosilicate]] [[glass|crown glass]]<br>(known as ''BK7'')||1.03961212||0.231792344||1.01046945||6.00069867×10<sup>&minus;3</sup>µm<sup>2</sup>|| 2.00179144×10<sup>&minus;2</sup>µm<sup>2</sup>||1.03560653×10<sup>2</sup>µm<sup>2</sup>
|-
|sapphire<br>(for [[ordinary wave]])||1.43134930||0.65054713||5.3414021||5.2799261×10<sup>&minus;3</sup>µm<sup>2</sup>|| 1.42382647×10<sup>&minus;2</sup>µm<sup>2</sup>||3.25017834×10<sup>2</sup>µm<sup>2</sup>
|-
|sapphire<br>(for [[extraordinary wave]])||1.5039759||0.55069141||6.5927379||5.48041129×10<sup>&minus;3</sup>µm<sup>2</sup>|| 1.47994281×10<sup>&minus;2</sup>µm<sup>2</sup>||4.0289514×10<sup>2</sup>µm<sup>2</sup>
|-
|[[Fused quartz|fused silica]]||0.696166300||0.407942600||0.897479400||4.67914826×10<sup>&minus;3</sup>µm<sup>2</sup>|| 1.35120631×10<sup>&minus;2</sup>µm<sup>2</sup>||97.9340025&nbsp;µm<sup>2</sup>
|}
 
== See also ==
*[[Cauchy's equation]]
*[[Kramers–Kronig relation]]
 
==References==
<references />
*W. Sellmeier, Zur Erklärung der abnormen Farbenfolge im Spectrum einiger Substanzen, ''Annalen der Physik und Chemie'' '''219''', 272-282 (1871).
 
==External links==
*[http://RefractiveIndex.INFO/ RefractiveIndex.INFO] Refractive index database featuring Sellmeier coefficients for many hundreds of materials.
*[http://www.calctool.org/CALC/phys/optics/sellmeier A browser-based calculator giving refractive index from Sellmeier coefficients.]
*[http://gallica.bnf.fr/ark:/12148/cb34462944f/date Annalen der Physik] - free Access, digitized by the French national library
 
[[Category:Optics]]
[[Category:Equations]]

Latest revision as of 02:45, 22 November 2014

It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.



Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.

At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.

Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.

Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.

Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.

Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.

Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.

In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.

If you have any type of inquiries regarding where and exactly how to utilize dentist DC, you can contact us at the website.

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