Forest ElemPhysics Optics ThinFilms - Revision history

Oborn: /* Example */

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Example

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 == Example==
-  Find the index of refraction of a fiber optic cable if 633 nm wavelength light enters it on the air side and the light inside the fiber is 452nm.
+Find the index of refraction of a fiber optic cable if 633 nm wavelength light enters it on the air side and the light inside the fiber is 452nm.
 :Answ: <math>n = \frac{\lambda_o}{\lambda} = \frac{ 633nm}{452nm}</math> = 1.4
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 http://physics.bu.edu/~duffy/semester2/c26_thinfilm.html
 =NonReflecting Thin Film=

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-Prperties of Refection and Refraction
+=Properties of Refection and Refraction=
 .) Waves reflect from higher index of refraction materials will have a half wave shift.
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 <math>\frac{\lambda_0} {\lambda} = \frac{v_o/f}{v/f} = \frac{c/n_0}{c/n} = \frac{n}{n_0} = n : n_0 =1 </math>if air

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 Thin Film of MgF2 on glass
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 ;So
-:<math>t_{Destructive} = \frac{m +\frac{1}{2}}{2n}</math>
+:<math>t_{Destructive} = \frac{m +\frac{1}{2}}{2n} \Rightarrow</math> Non-Reflecting
-:<math>t_{Constructive} = \frac{m}{2n}</math>
+:<math>t_{Constructive} = \frac{m}{2n} \Rightarrow</math>Reflecting
 [http://wiki.iac.isu.edu/index.php/Forest_ElemPhysics_Optics Go back] [[Forest_ElemPhysics_Optics]]

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 ;So
-:<math>t_{Destructive} = \frac{m +\frac{1}{2}}{2n}</math>:<math>t_{Constructive} = \frac{m}{2n}</math>
+:<math>t_{Destructive} = \frac{m +\frac{1}{2}}{2n}</math>
 [http://wiki.iac.isu.edu/index.php/Forest_ElemPhysics_Optics Go back] [[Forest_ElemPhysics_Optics]]

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 :The path difference between the waves = (Path difference from traveling in MgF2) - (Path difference from reflection)
-:(Path difference from reflection) = <math>\lambda_0</math>/2
+:Since both reflected waves have a phase shift we can neglect it and just focus on the path difference of the wave
 :(Path difference from traveling in MgF2) = 2 t = 2 <math>\times</math> thickness of MgF2 film
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 If we are interested in the
 ;Conditions for DESTRUCTIVE Interference
-:Then <math>2nt - \lambda_0/2 = (m) \lambda_0</math>
+:Then <math>2nt = (m + \frac{1}{2}) \lambda_0</math>
 [http://wiki.iac.isu.edu/index.php/Forest_ElemPhysics_Optics Go back] [[Forest_ElemPhysics_Optics]]

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 Consider the interference pattern observed when the wave from the MgF2 recombines with the reflect wave in the air.
-; The path difference between the waves = (Path difference from traveling in MgF2) - (Path difference from reflection)
+:The path difference between the waves = (Path difference from traveling in MgF2) - (Path difference from reflection)
-;(Path difference from reflection) = <math>\lambda_0</math>/2
+:(Path difference from reflection) = <math>\lambda_0</math>/2
-;(Path difference from traveling in MgF2) = 2 t = 2 <math>\times</math> thickness of MgF2 film
+:(Path difference from traveling in MgF2) = 2 t = 2 <math>\times</math> thickness of MgF2 film
 BUT
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 Let's instead use the effective distance d_o to represent the distance traveled in the MgF2 film if the wavelength didn't shorten.
-;d_0 = n \time t
+:d_0 = n \time t
 We can now treat the recombination of the light from the MgF2 as having the same wavelength as the light it is recombining with in air.
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 If we are interested in the
-:Conditions for DESTRUCTIVE Interference
+;Conditions for DESTRUCTIVE Interference
 :Then <math>2nt - \lambda_0/2 = (m) \lambda_0</math>
 [http://wiki.iac.isu.edu/index.php/Forest_ElemPhysics_Optics Go back] [[Forest_ElemPhysics_Optics]]

← Older revision		Revision as of 05:13, 20 April 2009
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	;The path difference between the waves =<math> 2nt - \lambda_0/2</math>		;The path difference between the waves =<math> 2nt - \lambda_0/2</math>
		+
		+	If we are interested in the
		+	:Conditions for DESTRUCTIVE Interference
		+	;Then 2nt - \lambda_0/2 = (m) \lambda_0

	[http://wiki.iac.isu.edu/index.php/Forest_ElemPhysics_Optics Go back] [[Forest_ElemPhysics_Optics]]		[http://wiki.iac.isu.edu/index.php/Forest_ElemPhysics_Optics Go back] [[Forest_ElemPhysics_Optics]]

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 This means that reflection on all the interfaces will have a half wavelength <math>(\pi)</math> phase shift because wave is reflected from a higher index of refraction both times.
-.) The wavelength shortens each time.
+Consider the interference pattern observed when the wave from the MgF2 recombines with the reflect wave in the air.
 [http://wiki.iac.isu.edu/index.php/Forest_ElemPhysics_Optics Go back] [[Forest_ElemPhysics_Optics]]

← Older revision		Revision as of 05:00, 20 April 2009
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	<math>n \equiv \frac{c}{v}</math>		<math>n \equiv \frac{c}{v}</math>

−	<math>\frac{\lambda_0} {\lambda} = \frac{v_o/f}{v/f} = \frac{n}{n_0} = n : n_0 =1 </math>if air	+	<math>\frac{\lambda_0} {\lambda} = \frac{v_o/f}{v/f} = \frac{c/n_0}{c/n} = \frac{n}{n_0} = n : n_0 =1 </math>if air