reerer Posted October 28, 2017 Posted October 28, 2017 The transmission and reflection equations of light are derived using light waves represented with (Hecht, p. 111), I = Io cos(k1x - wt) ĵ,...................................................................................116 R = Ro cos(k1x - wt) ĵ,...............................................................................117 T = To cos(-k2x + wt) ĵ,..............................................................................118 The incident (I), transmission (T) and reflection (R) light waves' (equ 116 - 118) interaction at the transmission and reflection surface (fig 18) is represented with, Io cos(k1x - wt) j + Ro cos(k1x - wt) j = To cos(- k2x + wt) j......................119 Using t = 0 and x = 0 equation 118 forms (Hecht, p. 113), (Klein, p. 570), Io + Ro = To.............................................................................................120 . The following equation (Hecht, p. 114), n1Io - n1Ro = n2To.................................................................................121 and equation 120 are used to derive the transmission and reflection equations, t = 2n1/ (n1 + n2)....................................................................................122 r = (n2 - n1) / (n1 + n2)............................................................................123 Using an air glass surface, n1 = 1 and n2 = 1.5, equation 121 forms, Io - Ro = 1.5To.......................................................................................124 Equations 120 and 121 are used to derive the transmission and reflection equations but the difference of the incident (Io) and reflection (Ro) maximum amplitudes (equ 124), derived using equation 121, forms a value that is greater than the sum (equ 120). ____________________________________________________________________________________________________________ Is my mathematics right?
Strange Posted October 28, 2017 Posted October 28, 2017 16 minutes ago, reerer said: Is my mathematics right? where did you copy it from?
swansont Posted October 29, 2017 Posted October 29, 2017 14 hours ago, Strange said: where did you copy it from? ! Moderator Note I second this request. Do not ignore it.
Sensei Posted October 29, 2017 Posted October 29, 2017 He said that in the first line. (Eugene) Hecht wrote couple books about Optics. https://www.amazon.com/Optics-5th-Eugene-Hecht/dp/0133977226
John Cuthber Posted October 29, 2017 Posted October 29, 2017 15 hours ago, reerer said: Is my mathematics right? As far as I can tell, it's Hecht's maths and he probably got it right. Why do you ask?
reerer Posted October 30, 2017 Author Posted October 30, 2017 (edited) On 10/29/2017 at 4:57 AM, swansont said: ! Moderator Note I second this request. Do not ignore it. I am the author of everything I post except for the quotations. Example, the equations of the following derivation are not mine but everything else I wrote, personally. Swear to God. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- The quantum mechanic step potential method is used to derive the transmission and reflection equations (Eisberg, p. 211), (McGervey, p. 102). The interaction of the incident, reflection and transmission light waves at the surface interface (x = 0) is represented with (fig 18), Ioe-ik1x + Roeik1x = Toe-ik2x ....................................................125 Using x = 0 in equation 125 the following equation is formed, Io + Ro = To........................................................................126 Differentiating equations 125 with respect to d/dx then using x = 0 forms, k1Io - k1Ro = k2To...............................................................127 Replacing k with n since k is proportional to n equation 127 forms, n1Io - n1Ro = n2To..............................................................128 Equations 127 and 128 are used in the derivation of the transmission and reflection equations. t = 2n1 / (n1 + n2) ..............................................................129 r = (n2 - n1) / (n1 + n2) ......................................................130 Using n1 = 1 and n2 = 1.5 in equation 128, Io - Ro = (1.5)To ..............................................................131 Using a air/glass interface, the difference of the incident and reflection light waves' maximum amplitudes (equ 131) is greater then the sum (equ 126) which is mathematically invalid and proves the quantum mechanics step potential derivation of the transmission and reflection equations using equations 129 and 130 is invalid and I certainly acknowledge that if I am wrong that it is a mistake to be wrong. Edited October 30, 2017 by reerer
swansont Posted October 30, 2017 Posted October 30, 2017 2 hours ago, reerer said: I am the author of everything I post except for the quotations. Example, the equations of the following derivation are not mine but everything else I wrote, personally. Swear to God. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- The quantum mechanic step potential method is used to derive the transmission and reflection equations (Eisberg, p. 211), (McGervey, p. 102). The interaction of the incident, reflection and transmission light waves at the surface interface (x = 0) is represented with (fig 18), ! Moderator Note The equation numbers start at arbitrary values. Same with the figure numbers and page references. The implication of your statement is that you have written up a manuscript, numbered and referenced it, added figures, and are quoting from it. That's what's going on?
reerer Posted October 30, 2017 Author Posted October 30, 2017 1 hour ago, swansont said: ! Moderator Note The equation numbers start at arbitrary values. Same with the figure numbers and page references. The implication of your statement is that you have written up a manuscript, numbered and referenced it, added figures, and are quoting from it. That's what's going on? I am making up the numbers and figure numbers as I go along. Sorry for the confussion.
Strange Posted October 30, 2017 Posted October 30, 2017 35 minutes ago, reerer said: I am making up the numbers and figure numbers as I go along. Why? Why start at 116? And why include figure numbers when there are no figures?
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