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Matrices in Paraxial Optics - Coggle Diagram
Matrices in Paraxial Optics
A ray can be defined by its height and its direction
(the angle it makes with the optical
axis)
Translational Matrix
Simple tanslation of a ray in a homogeneous medium is take into consideration
Translation from point 0 to 1 with paraxial approximation :
αi = α0 and y1 = y0 + L tan α0 = y0 L α0
Rewrite the equation :
Refraction Matrix
A refraction of a ray at a spherical interface is take into consideration (paraxial approximation):
Ray coordinates before refraction (y,a)
Ray coordinates after refraction (y',a')
Paraxial form of Snell's Law (n theta = n' theta'):
Reflection Matrix
Ray coordinates before refraction (y,a)
Ray coordinates after refraction (y',a')
Connect (y',a') to (y,a) by a ray transfer matrix for reflection by a concave mirror
Sign convention for angles :
(+) pointing upward
(-) pointing downward
Eliminate theta and theta' by using theta=theta' to get:
