Glass Material IOR and Dispersion - Revision history

CodeHD: fix a wrong wavelength

2020-11-01T23:24:30Z

fix a wrong wavelength

← Older revision		Revision as of 01:24, 2 November 2020
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	[[File:abbe_old.png\|x28px]]		[[File:abbe_old.png\|x28px]]

	where the three wavelengths are d = ~~589~~.3 nm, F = 486.12 nm and C = 656.27 nm. An alternative definition is based on slightly different wavelengths:		where the three wavelengths are d = 587.56 nm, F = 486.13 nm and C = 656.27 nm. An alternative definition is based on slightly different wavelengths:

	[[File:abbe_new.png\|x30px]]		[[File:abbe_new.png\|x30px]]

CodeHD: remove obsolete info

2020-10-31T23:43:44Z

remove obsolete info

← Older revision		Revision as of 01:43, 1 November 2020
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	'''Important:'''<br>		'''Important:'''<br>
	a) The usual convention, used also by LuxCore, is to calculate with wavelength in units of micrometers.<br>		a) The usual convention, used also by LuxCore, is to calculate with wavelength in units of micrometers.<br>
	b) Due to a different naming convention in the reference for the LuxCore implementation, the variables in the source code and tooltipps in BlendLuxCore currently ask for „Cauchy-C“ as the dispersion parameter instead of „Cauchy-B“.<br>		b) The Cauchy-A term is the asymptotical refractive index at high wavelengths. It is therefore smaller than the refractive index at the center of the visible spectrum, which is usually the IOR-value quoted for materials if nothing else is specified.
	c) The Cauchy-A term is the asymptotical refractive index at high wavelengths. It is therefore smaller than the refractive index at the center of the visible spectrum, which is usually the IOR-value quoted for materials if nothing else is specified.

	===The Sellmeier Equation===		===The Sellmeier Equation===

CodeHD: finishing IOR table

2020-10-31T23:26:18Z

finishing IOR table

← Older revision		Revision as of 01:26, 1 November 2020
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	The aim of this article is to present an overview of glass dispersion, how it is quantified and used in the LuxCore glass material to model dispersion, and how to get the correct numbers to use. The focus here is on using the data and models in the physically correct way. For artistic purposes, you may want to deviate from the described methods.		The aim of this article is to present an overview of glass dispersion, how it is quantified and used in the LuxCore glass material to model dispersion, and how to get the correct numbers to use. The focus here is on using the data and models in the physically correct way. For artistic purposes, you may want to deviate from the described methods.

	'''For most ~~people~~, the most interesting sections will be [[#Refractive Index and Dispersion Data\|Refractive Index and Dispersion Data]], where a list of selected parameters is provided, and section [[#Conversion from Abbe Number to Cauchy\|Conversion from Abbe Number to Cauchy]], where formulas to compute BlendLuxCore IOR and Dispersion from a pair of refractive index and Abbe-number are given.'''		'''For most readers, the most interesting sections will be [[#Refractive Index and Dispersion Data\|Refractive Index and Dispersion Data]], where a list of selected parameters is provided, and section [[#Conversion from Abbe Number to Cauchy\|Conversion from Abbe Number to Cauchy]], where formulas to compute BlendLuxCore IOR and Dispersion from a pair of refractive index and Abbe-number are given.'''

	==Introduction==		==Introduction==
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	A database of raw data for many materials can be found at [https://refractiveindex.info/ https://refractiveindex.info/].		A database of raw data for many materials can be found at [https://refractiveindex.info/ https://refractiveindex.info/].

	Below is a list of a few common materials with the IOR and dispersion settings for BlendLuxCore.		Below is a list of a few common materials with the IOR and dispersion settings for BlendLuxCore.

	{\| class="wikitable"		{\| class="wikitable"
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	\|0.00425		\|0.00425
	\|-		\|-
	~~\|Lead Crystal Glass~~		\|Acrylic (PMMA)
	~~\|1.xx~~		\|1.4767
	~~\|0.0xx~~		\|0.0048
	\|-
	\|Acrylic
	\|1.xx
	~~\|0.0xx~~
	\|-
	~~\|Epoxy Resin~~
	~~\|1.xx~~
	\|0.~~0xx~~
	\|-		\|-
	\|Prism Glass (N-SF11)		\|Prism Glass (N-SF11)
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	\|2.3818		\|2.3818
	\|0.0121		\|0.0121
			\|-
			\|Sapphire
			\|1.7522
			\|0.0055
	\|}		\|}

CodeHD: Small updates

2020-10-30T20:41:34Z

Small updates

← Older revision		Revision as of 22:41, 30 October 2020
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	The aim of this article is to present an overview of glass dispersion, how it is quantified and used in the LuxCore glass material to model dispersion, and how to get the correct numbers to use. The focus here is on using the data and models in the physically correct way. For artistic purposes, you may want to deviate from the described methods.		The aim of this article is to present an overview of glass dispersion, how it is quantified and used in the LuxCore glass material to model dispersion, and how to get the correct numbers to use. The focus here is on using the data and models in the physically correct way. For artistic purposes, you may want to deviate from the described methods.

			'''For most people, the most interesting sections will be [[#Refractive Index and Dispersion Data\|Refractive Index and Dispersion Data]], where a list of selected parameters is provided, and section [[#Conversion from Abbe Number to Cauchy\|Conversion from Abbe Number to Cauchy]], where formulas to compute BlendLuxCore IOR and Dispersion from a pair of refractive index and Abbe-number are given.'''

	==Introduction==		==Introduction==
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	[[File:abbeconvertB.png\|x28px]]		[[File:abbeconvertB.png\|x28px]]

	With the Cauchy-B parameter, the Cauchy-A parameter can be ~~converted~~. In this case, slightly different numbers must be used depending on the Abbe-definition. However, the error would be small, as B is small.		With the Cauchy-B parameter, the Cauchy-A parameter can be calculated. In this case, slightly different numbers must be used depending on the Abbe-definition. However, the error would be small, as B is small.

	[[File:abbeconvertA.png\|x14px]]		[[File:abbeconvertA.png\|x14px]]

	The Figure below shows an ~~exmaple~~ plot ~~of data~~ for ~~the~~ N-BK7 optical glass, ~~compared~~ with Cauchy-~~fits~~ derived from the two Abbe-number definitions ~~in the top panel~~. The bottom panel shows the relative error between the two definitions, as well as with the much better fitting Sellmeier equation. It can be seen that the error is below 0.05% across the visible spectrum.		The Figure below shows an example plot for N-BK7 optical glass. In the top panel, a comparison with Cauchy-formulas derived from the two Abbe-number definitions is shown. The bottom panel shows the relative error between the two definitions, as well as with the much better fitting Sellmeier equation. It can be seen that the error is below 0.05% across the visible spectrum, and the results of the two Abbe-number pairs are even much smaller.

			'''In other words: Don't worry too much about which Abbe-definition your numbers follow, just use the equations described above.'''

	[[File:cauchyplot.png\|600px\|]]<br>		[[File:cauchyplot.png\|600px\|]]<br>

CodeHD: Add wikipedia links

2020-10-28T19:04:44Z

Add wikipedia links

← Older revision		Revision as of 21:04, 28 October 2020
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	==Introduction==		==Introduction==

	Glasses have an important property called the Index Of Refraction (IOR). When a light ray encounters a change in IOR, e.g. at the surface of a piece of glass, the direction of the ray is changed according to Snell‘s law:		Glasses have an important property called the [https://en.wikipedia.org/wiki/Refractive_index Index Of Refraction] (IOR). When a light ray encounters a change in IOR, e.g. at the surface of a piece of glass, the direction of the ray is changed according to [https://en.wikipedia.org/wiki/Snell%27s_law Snell‘s law]:

	[[File:Snellslaw.png\|x20px]]<br>		[[File:Snellslaw.png\|x20px]]<br>
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	where n<sub>1</sub> and n<sub>2</sub> are the refractive indices outside and inside the glass, and θ<sub>1</sub> and θ<sub>2</sub> the angles between the surface normal vector and the rays outside and inside the glass.		where n<sub>1</sub> and n<sub>2</sub> are the refractive indices outside and inside the glass, and θ<sub>1</sub> and θ<sub>2</sub> the angles between the surface normal vector and the rays outside and inside the glass.

	For real materials, the IOR is a function of the wavelength λ of light. This property is called dispersion. For example, the IOR of N-BK7 glass, a common glass for laboratory optics, varies between n = 1.53 at a λ = 400 nm, to n = 1.51 at λ = 800 nm. This may not seem a big difference, but it has significant impact on imaging optics.		For real materials, the IOR is a function of the wavelength λ of light. This property is called [https://en.wikipedia.org/wiki/Dispersion_(optics) dispersion]. For example, the IOR of [https://shop.schott.com/advanced_optics/Products/Optical-Glass/Optical-Glass/Boron-Crown/SCHOTT-N-BK7%C2%AE/c/optical-glass/glass-SCHOTT%20N-BK7%C2%AE N-BK7] glass, a common glass for laboratory optics, varies between n = 1.53 at a λ = 400 nm, to n = 1.51 at λ = 800 nm. This may not seem a big difference, but it has significant impact on imaging optics.

	==Quantifying Dispersion==		==Quantifying Dispersion==
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	===The Abbe number===		===The Abbe number===

	A very common quantification is the Abbe number, denoted by ν, which is calculated from the refractive index at three differnt wavelengths:		A very common quantification is the [https://en.wikipedia.org/wiki/Abbe_number Abbe number], denoted by ν, which is calculated from the refractive index at three differnt wavelengths:

	[[File:abbe_old.png\|x28px]]		[[File:abbe_old.png\|x28px]]
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	===The Cauchy Equation===		===The Cauchy Equation===

	The Cauchy equation provides an approximate formula for the dispersion of light. The equation has the following form:		The [https://en.wikipedia.org/wiki/Cauchy%27s_equation Cauchy equation] provides an approximate formula for the dispersion of light. The equation has the following form:

	[[File:cauchy_multi.png\|x25px]]		[[File:cauchy_multi.png\|x25px]]
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	===The Sellmeier Equation===		===The Sellmeier Equation===

	Like the Cauchy equation, the Sellmeier equation is a formula describing the refractive index as a function of wavelength. It is more complex and suited to describe the refractive index over a wider range of wavelengths:		Like the Cauchy equation, the [https://en.wikipedia.org/wiki/Sellmeier_equation Sellmeier equation] is a formula describing the refractive index as a function of wavelength. It is more complex and suited to describe the refractive index over a wider range of wavelengths:

	[[File:sellmeyer.png\|x30px]]<br>		[[File:sellmeyer.png\|x30px]]<br>

CodeHD: started work on table; fix Sellmeier typo

2020-10-28T18:42:43Z

started work on table; fix Sellmeier typo

@@ Line 51: / Line 51: @@
 c) The Cauchy-A term is the asymptotical refractive index at high wavelengths. It is therefore smaller than the refractive index at the center of the visible spectrum, which is usually the IOR-value quoted for materials if nothing else is specified.
-===The Sellmeyer Equation===
+===The Sellmeier Equation===
-Like the Cauchy equation, the Sellmeyer equation is a formula describing the refractive index as a function of wavelength. It is more complex and suited to describe the refractive index over a wider range of wavelengths:
+Like the Cauchy equation, the Sellmeier equation is a formula describing the refractive index as a function of wavelength. It is more complex and suited to describe the refractive index over a wider range of wavelengths:
 [[File:sellmeyer.png|x30px]]<br>
@@ Line 96: / Line 96: @@
 A database of raw data for many materials can be found at [https://refractiveindex.info/ https://refractiveindex.info/].
 ==Further Reading==

CodeHD: fix missing units, add note on units for cauchy equation

2020-10-24T16:26:08Z

fix missing units, add note on units for cauchy equation

← Older revision		Revision as of 18:26, 24 October 2020
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	[[File:abbe_new.png\|x30px]]		[[File:abbe_new.png\|x30px]]

	where the three wavelengths are e = 546.07, F‘ = 479.99 and C‘ = 643.85.		where the three wavelengths are e = 546.07 nm, F‘ = 479.99 nm and C‘ = 643.85 nm.

	'''Important:'''<br>		'''Important:'''<br>
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	'''Important:'''<br>		'''Important:'''<br>
	a) Due to a different naming convention in the reference for the LuxCore implementation, the variables in the source code and tooltipps in BlendLuxCore currently ask for „Cauchy-C“ as the dispersion parameter instead of „Cauchy-B“.<br>		a) The usual convention, used also by LuxCore, is to calculate with wavelength in units of micrometers.<br>
	b) The Cauchy-A term is the asymptotical refractive index at high wavelengths. It is therefore smaller than the refractive index at the center of the visible spectrum, which is usually the IOR-value quoted for materials if nothing else is specified.		b) Due to a different naming convention in the reference for the LuxCore implementation, the variables in the source code and tooltipps in BlendLuxCore currently ask for „Cauchy-C“ as the dispersion parameter instead of „Cauchy-B“.<br>
			c) The Cauchy-A term is the asymptotical refractive index at high wavelengths. It is therefore smaller than the refractive index at the center of the visible spectrum, which is usually the IOR-value quoted for materials if nothing else is specified.

	===The Sellmeyer Equation===		===The Sellmeyer Equation===

CodeHD: Add text on conversion equations

2020-10-24T16:02:26Z

Add text on conversion equations

← Older revision		Revision as of 18:02, 24 October 2020
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	This equation already provides a good fit to many real glasses in the visible spectrum.		This equation already provides a good fit to many real glasses in the visible spectrum.

	Since this form only depends on the two coefficients A and B, it is possible to convert them from a pair of Abbe number and refactive. The conversion algorithm is given below in section ().		Since this form only depends on the two coefficients A and B, it is possible to convert them from a pair of Abbe number and refactive. The conversion algorithm is given below in section [[#Conversion from Abbe Number to Cauchy\|Conversion from Abbe Number to Cauchy]].

	'''Important:'''<br>		'''Important:'''<br>
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	==Conversion from Abbe Number to Cauchy==		==Conversion from Abbe Number to Cauchy==

	~~TBD~~...		The Cauchy-coefficents A and B can be calculated from a pair of Abbe number and refractive index, indexed e and d as described in section [[#The Abbe number\|The Abbe number]]. First, the Cauchy-B parameter is calculated. The following equation is given for the d-, F- and C-wavelength definition. However, the factor of 0.52 also roughly results with the F'- and C'-wavelengths, so that the equation can be applied in both cases:

			[[File:abbeconvertB.png\|x28px]]

			With the Cauchy-B parameter, the Cauchy-A parameter can be converted. In this case, slightly different numbers must be used depending on the Abbe-definition. However, the error would be small, as B is small.

			[[File:abbeconvertA.png\|x14px]]

			The Figure below shows an exmaple plot of data for the N-BK7 optical glass, compared with Cauchy-fits derived from the two Abbe-number definitions in the top panel. The bottom panel shows the relative error between the two definitions, as well as with the much better fitting Sellmeier equation. It can be seen that the error is below 0.05% across the visible spectrum.

			[[File:cauchyplot.png\|600px\|]]<br>

			==Refractive Index and Dispersion Data==
			A database of raw data for many materials can be found at [https://refractiveindex.info/ https://refractiveindex.info/].


	==Further Reading==		==Further Reading==

CodeHD: Insert equations, images, fix some text

2020-10-23T16:11:47Z

Insert equations, images, fix some text

← Older revision		Revision as of 18:11, 23 October 2020
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	The aim of this article is to present an overview of glass dispersion, how it is quantified and used in the LuxCore glass material to model dispersion, and how . The focus here is on using the data and models in the physically correct way. For artistic purposes, you may want to deviate from the described methods.		The aim of this article is to present an overview of glass dispersion, how it is quantified and used in the LuxCore glass material to model dispersion, and how to get the correct numbers to use. The focus here is on using the data and models in the physically correct way. For artistic purposes, you may want to deviate from the described methods.

	==Introduction==		==Introduction==
Line 5:		Line 5:
	Glasses have an important property called the Index Of Refraction (IOR). When a light ray encounters a change in IOR, e.g. at the surface of a piece of glass, the direction of the ray is changed according to Snell‘s law:		Glasses have an important property called the Index Of Refraction (IOR). When a light ray encounters a change in IOR, e.g. at the surface of a piece of glass, the direction of the ray is changed according to Snell‘s law:

	[[File:Snellslaw.png\|~~200px\|frameless\|left~~]]<br>		[[File:Snellslaw.png\|x20px]]<br>

	where n<sub>1</sub> and n<sub>2</sub> are the refractive indices outside and inside the glass, and &#~~x0398~~;<sub>1</sub> and &#~~x0398~~;<sub>2</sub> the angles between the surface normal vector and the rays outside and inside the glass.		where n<sub>1</sub> and n<sub>2</sub> are the refractive indices outside and inside the glass, and θ<sub>1</sub> and θ<sub>2</sub> the angles between the surface normal vector and the rays outside and inside the glass.

	For real materials, the IOR is a function of the wavelength λ of light. This property is called dispersion. For example, the IOR of N-BK7 glass, a common glass for laboratory optics, varies between n = 1.53 at a λ = 400 nm, to n = 1.51 at λ = 800 nm. This may not seem a big difference, but it has significant impact on imaging optics.		For real materials, the IOR is a function of the wavelength λ of light. This property is called dispersion. For example, the IOR of N-BK7 glass, a common glass for laboratory optics, varies between n = 1.53 at a λ = 400 nm, to n = 1.51 at λ = 800 nm. This may not seem a big difference, but it has significant impact on imaging optics.
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	===The Abbe number===		===The Abbe number===

	A very common quantification is the Abbe number, denoted by nu, which is calculated from the refractive index at three differnt wavelengths:		A very common quantification is the Abbe number, denoted by ν, which is calculated from the refractive index at three differnt wavelengths:

	~~nuD = (nD – 1)/(nF – nC)~~		[[File:abbe_old.png\|x28px]]

	where the three wavelengths are D = 589.3, F = 486.12 and C = 656.27. An alternative definition is based on slightly different wavelengths:		where the three wavelengths are d = 589.3 nm, F = 486.12 nm and C = 656.27 nm. An alternative definition is based on slightly different wavelengths:

	~~nue = (ne – 1)/(nF‘ – nC‘)~~		[[File:abbe_new.png\|x30px]]

	where the three wavelengths are e = 546.07, F‘ = 479.99 and C‘ = 643.85.		where the three wavelengths are e = 546.07, F‘ = 479.99 and C‘ = 643.85.

	Important:		'''Important:'''<br>
	a) The Abbe number is an index value derived from three specific data points. As such, it makes no statement on how the refractive index varies between these points.		a) The Abbe number is an index value derived from three specific data points. As such, it makes no statement on how the refractive index varies between these points.<br>
	b) When working with the Abbe number, check which of the two definitions is used.		b) When working with the Abbe number, check which of the two definitions is used.

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	The Cauchy equation provides an approximate formula for the dispersion of light. The equation has the following form:		The Cauchy equation provides an approximate formula for the dispersion of light. The equation has the following form:

	~~N(lambda) = A + B/lambda^2 + C/lambda^4 + ..~~.		[[File:cauchy_multi.png\|x25px]]

	by convention, the wavelength must be used in units of micrometers!		by convention, the wavelength must be used in units of micrometers!
	The glass material in LuxCore uses only the first two terms of the equation, i.e.		The glass material in LuxCore uses only the first two terms of the equation, i.e.

	~~N(lambda) = A + B/lambda^2~~		[[File:cauchy_2term.png\|x25px]]

	This equation already provides a good fit to many real glasses in the visible spectrum.		This equation already provides a good fit to many real glasses in the visible spectrum.
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	Since this form only depends on the two coefficients A and B, it is possible to convert them from a pair of Abbe number and refactive. The conversion algorithm is given below in section ().		Since this form only depends on the two coefficients A and B, it is possible to convert them from a pair of Abbe number and refactive. The conversion algorithm is given below in section ().

	Important:		'''Important:'''<br>
	a) Due to a different naming convention in the reference for the LuxCore implementation, the variables in the source code and tooltipps in BlendLuxCore currently ask for „Cauchy-C“ as the dispersion parameter instead of „Cauchy-B“.		a) Due to a different naming convention in the reference for the LuxCore implementation, the variables in the source code and tooltipps in BlendLuxCore currently ask for „Cauchy-C“ as the dispersion parameter instead of „Cauchy-B“.<br>
	b) The Cauchy-A term is the asymptotical refractive index at high wavelengths. It is therefore smaller than the refractive index at the center of the visible spectrum, which is usually the IOR-value quoted for materials if nothing else is specified.		b) The Cauchy-A term is the asymptotical refractive index at high wavelengths. It is therefore smaller than the refractive index at the center of the visible spectrum, which is usually the IOR-value quoted for materials if nothing else is specified.

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	Like the Cauchy equation, the Sellmeyer equation is a formula describing the refractive index as a function of wavelength. It is more complex and suited to describe the refractive index over a wider range of wavelengths:		Like the Cauchy equation, the Sellmeyer equation is a formula describing the refractive index as a function of wavelength. It is more complex and suited to describe the refractive index over a wider range of wavelengths:

	…		[[File:sellmeyer.png\|x30px]]<br>

	As for the Cauchy equation, further terms could be used. Data sheets for optical glasses usually give the six coefficients of the above form.		As for the Cauchy equation, further terms could be used. Data sheets for optical glasses usually give the six coefficients of the above form.
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	The concept of relative partial dispersions is similar to the Abbe number, but using another pair of refractive index difference at certain wavelengths in the numerator of the equation.		The concept of relative partial dispersions is similar to the Abbe number, but using another pair of refractive index difference at certain wavelengths in the numerator of the equation.

	Even simpler, the refractive index difference ~~can be used directly~~. A commonly found example is a dispersion value of 0.044 for Diamond. This is of the same order of magnitude as the Cauchy-B coefficent B = 0.012, and thus often quoted and used		Even simpler, the refractive index difference between red and blue light is sometimes given. A commonly found example is a dispersion value of 0.044 for Diamond. This is of the same order of magnitude as the Cauchy-B coefficent B = 0.012, and thus often quoted and used.

			==Dispersion in LuxCore and Tipps==

	~~==Dispersion~~ in LuxCore ~~and Tipps==~~		As mentioned in the previous section, LuxCore uses a two-term Cauchy equation to model the refractive index.

	~~As mentioned in the previous section, LuxCore uses a two-term Cauchy equation to model the refractive index.~~ Therefore, in (Blend)LuxCore, the correct way to input values is to set the Cauchy-A coefficient as IOR, and the Cauchy-B coefficient as dispersion.		'''Therefore, in (Blend)LuxCore, the correct way to input values is to set the Cauchy-A coefficient as IOR, and the Cauchy-B coefficient as dispersion.'''

	For artistic applications, it should be fine to use the IOR at a visible wavelength instead of the Cauchy-A term. Likewise, a higher dispersion value may be used to compensate for limitations of the rendering process, like SDS caustics or fully specular paths.		For artistic applications, it should be fine to use the IOR at a visible wavelength instead of the Cauchy-A term. Likewise, a higher dispersion value may be used to compensate for limitations of the rendering process, like SDS caustics or fully specular paths.

	The following image shows a comparison of a diamond rendered at ~~different view angles and~~ with different ~~light sources, as well as with~~ B=0, B = 0.0121 and B = 0.044.		The following image shows a comparison of a diamond rendered at with different dispersion values of B = 0 (no dispersion), B = 0.0121 (physically correct) and B = 0.044 (often quoted value). The IOR was adapted so that the refractive index at 550 nm remains constant and the caustics remain centered in the same location.

	...		[[File:diamonddispersion.gif]]<br>

	==Conversion from Abbe Number to Cauchy==		==Conversion from Abbe Number to Cauchy==

			TBD...

	==Further Reading==		==Further Reading==
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	Some manufacturers of optical glasses and lens systems have published technical documents that may be helpful to further understand dispersion and how it is measured.		Some manufacturers of optical glasses and lens systems have published technical documents that may be helpful to further understand dispersion and how it is measured.

	[https://www.schott.com/d/advanced_optics/02ffdb0d-00a6-408f-84a5-19de56652849/1.2/tie_29_refractive_index_and_dispersion_eng.pdf Schott TIE-29]		[https://www.schott.com/d/advanced_optics/02ffdb0d-00a6-408f-84a5-19de56652849/1.2/tie_29_refractive_index_and_dispersion_eng.pdf Schott TIE-29: Refractive Index and Dispersion]

			[http://opticampus.opti.vision/files/memo_on_reference_wavelengths.pdf Zeiss Memorandum on reference wavelengths]

	[https://www.schott.com/advanced_optics/german/knowledge-center/technical-articles-and-tools/tie.html Schott TIE Document collection]		[https://www.schott.com/advanced_optics/german/knowledge-center/technical-articles-and-tools/tie.html Schott TIE Document collection]

	~~[http://opticampus.opti.vision/files/memo_on_reference_wavelengths.pdf Zeiss Memorandum on reference wavelengths]~~

CodeHD: Updating/testing equations and symbols

2020-10-23T15:29:33Z

Updating/testing equations and symbols

← Older revision		Revision as of 17:29, 23 October 2020
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	Glasses have an important property called the Index Of Refraction (IOR). When a light ray encounters a change in IOR, e.g. at the surface of a piece of glass, the direction of the ray is changed according to Snell‘s law:		Glasses have an important property called the Index Of Refraction (IOR). When a light ray encounters a change in IOR, e.g. at the surface of a piece of glass, the direction of the ray is changed according to Snell‘s law:

			[[File:Snellslaw.png\|200px\|frameless\|left]]<br>

	<~~math~~>~~n_1 {\text{sin}}(\Theta_1) = n_2 {\text{sin}}(\Theta_2)~~</~~math~~>		where n<sub>1</sub> and n<sub>2</sub> are the refractive indices outside and inside the glass, and Θ<sub>1</sub> and Θ<sub>2</sub> the angles between the surface normal vector and the rays outside and inside the glass.

	where <math>n_1</math> and <math>n_2</math> are the refractive indices outside and inside the glass, and <math>\Theta_1</math> and <math>\Theta_2</math> the angles between the surface normal vector and the rays outside and inside the glass.		For real materials, the IOR is a function of the wavelength λ of light. This property is called dispersion. For example, the IOR of N-BK7 glass, a common glass for laboratory optics, varies between n = 1.53 at a λ = 400 nm, to n = 1.51 at λ = 800 nm. This may not seem a big difference, but it has significant impact on imaging optics.

	For real materials, the IOR is a function of the wavelength of light. This property is called dispersion. For example, the IOR of N-BK7 glass, a common glass for laboratory optics, varies between ~~<math>~~n = 1.53~~</math>~~ at a ~~wavelength of~~ 400 nm, to ~~<math>~~n = 1.51~~</math>~~ at 800 nm. This may not seem a big difference, but it has significant impact on imaging optics.

	==Quantifying Dispersion==		==Quantifying Dispersion==