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Trans­ition­ing from Elec­tro­mag­net­ism to Optics begins with Maxwell’s Equa­tions and attempts to make the jump from Elec­tro­mag­net­ism to Geo­met­ric and Wave Optics. This is a step which is per­haps over­looked in tra­di­tion­al optics courses and leaves stu­dents with some confusion. ’

How does all my hard work with math­em­at­ics end up with the simple light ray and Snell’s Law?!’ Well hope­fully the phys­ics tutori­al videos below will help you with that trans­ition from Elec­tro­mag­net­ism to Optics!

Return to Elec­tro­mag­net­ism and Optics

Video # Video Tutori­al Title Remarks
1 Trav­el­ling Waves (x+-vt) 1/2 Why ψ(x) is a sta­tion­ary wave but ψ(x+-vt) is a trav­el­ling wave
2 Trav­el­ling Waves (x+-vt) 2/2 Why ψ(x) is a sta­tion­ary wave but ψ(x+-vt) is a trav­el­ling wave (older ver­sion of video)
3 The Wave Equation A dis­cus­sion and deriv­a­tion of one of the most import­ant equa­tions in physics
4 Har­mon­ic Sinus­oid­al Waves Dis­cuss­ing the com­pon­ents of the argu­ment of the wave­func­tion cos/sin(x+-vt)
5 Com­plex Num­bers for Optics All of the math­em­at­ics for optics involves the use of com­plex numbers
6 Com­plex Rep­res­ent­a­tion of Waves Mov­ing from the cosine/sine rep­res­ent­a­tion of the wave­func­tion to com­plex exponentials
7 Group and Phase Velocity Group velo­city for the wave­pack­et; phase velo­city for the phase of the com­pon­ent waves
8  Maxwell’s Equa­tions  Elec­tro­mag­net­ism to Optics
9  The Elec­tro­mag­net­ic Wave Equation  Build­ing upon video #3 and deriv­ing the EM wave equation
10 Con­vert­ing Cos and Sin to Com­plex Exponential Using Euler’s Equa­tion to con­vert cosine and sine to com­plex exponentials
11 Sep­ar­a­tion of Vari­ables Solu­tion to Dif­fer­en­tial Equations Intro­du­cing a very power­ful tech­nique for solv­ing dif­fer­en­tial equations
12    
13 Solv­ing the EM Wave Equation Using the tech­nique out­lined in video #11 to solve the equa­tion and find the wavefunction
14 Plane Waves Plane waves = light rays and Geo­met­ric Optics
15 Mag­net­ic Field is Per­pen­dic­u­lar to the Wave-vector One of the more inter­est­ing math­em­at­ic­al res­ults from the wave equation
16 a The Elec­tric and Mag­net­ic Fields are Per­pen­dic­u­lar 1/2 Build­ing upon the res­ult from video #15
16 b The Elec­tric and Mag­net­ic Fields are Per­pen­dic­u­lar 2/2 An older ver­sion of video #16 a
17 a Energy in the EM Field One of the most import­ant the­or­ems from clas­sic­al mechanics!
17 b The Poyn­t­ing Vector The energy per unit time per unit area being trans­ferred by the EM field
17 c Elec­tro­mag­net­ic Energy Density Energy per unit volume
18 Elec­tric Field Bound­ary Conditions  
19 Mag­net­ic Field Bound­ary Conditions  
20 Light Incid­ent Nor­mally Upon a Bound­ary 1/2 Reflec­tion and trans­mis­sion at nor­mal incidence
21 Light Incid­ent Nor­mally Upon a Bound­ary 2/2 Reflec­tion co-effi­cient at nor­mal incidence
22 Deriv­a­tion of Snell’s Law Deriv­a­tion using EM rather than pins/paper and a block of glass!
23 Fres­nel Equa­tions 1/2 Light incid­ent upon a bound­ary at oblique incidence
24 Fres­nel Equa­tions 2/2 Light incid­ent upon a bound­ary at oblique incidence

 

 kahn academy phys­ics fres­nel snell snell’s law irra­di­ance ray optics  kahn academy phys­ics fres­nel snell snell’s law irra­di­ance ray optics  kahn academy phys­ics fres­nel snell snell’s law irra­di­ance ray optics elec­tro­mag­net­ism to optics

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