ch 9 light as rays Flashcards
what does this theory misss
only focuses on macroscopic flow of light energy
ignores diffraciton phenomena
Eikonal eqn from
Maxwell eqn in short wavelength limit
features of interest»wavelength of light (deriv of eikonal)
the eikonal eqn governs direction of rays in a medium where n changes with potision. controls the formation of images
Fermat principle
Light trabrls from pt A to B following path that takes minimum time
can be derived from eikonal eqn
Paraxial ray theory
restrcts rays to travel nearly // to opt axis
Lensmakes formula
1/f = 1/d0 +1/di
curved mirror or thin lens int he paraxial approx
Deriv of eikonal
Start with WE in isotropic but with n(r)
sub in pw soln with k=kvac and compute lapcian
note shorrt wavelength approx -> 1/k and 1/k^2 =0
gives eikonal
eikonal tells us
DE tells with changing n predicts how a ray will propogate
poynting vector // s (direction of eikonal R(r))
Rays
Collection of vectors s distributed thorugh space
Optical path length
OPL (from A to B) = int (A to B) n dl
needs to be minimised
Rel OPL geo PL
Not same as a ray travleing thorugh thicker amt of lens get extra time added on even though maybe a geometrically shorter lenth
How to derive snell law from OPL
pt x1y1 to x2y2 in 2nd medium set x1,x2 fixed ytot = y1+y2 variable indicually use trig to get OPL (pythag) write ito yi,ytot minimize OPL d/dyi recognise the sin(theta_i) gives snells law
where does image occur
When all rays froma point on an object ocnverge
to a correspd point on the image
What happens when not // and the approximations violated
Clarity of image poor - > abberations present
