Snell's Law.

To do:
(i) Add polarization.
(ii) Remove internally reflected ray at T_i>T_c properly.
(iii) Re-implement as vectors rather than as lines? Can then have arrowheads, scale lengths.

Indices of refraction.

N_1=slider([1,2])

N_2=slider([1,2])

Angles of incidence, refraction, and reflection. Critical angle (total internal reflection). Brewster's angle (perfect polarization by reflection).

T=slider([0,1])

T_i=T*pi/2,T_r=asin([N_1/N_2*sin(T_i)]),T_R=T_i,T_c=asin([N_2/N_1]),T_B=atan([N_2/N_1])

Medium 1 above, medium 2 below. Normal.

y<0

x=0

Incident, reflected, and refracted rays.

y=[-1/tan(T_i)]*x,x<0

y=[1/tan(T_R)]*x,x>0

y=[-1/tan(T_r)]*x,x>0

Critical angle for total internal reflection.

180/pi*T_c

y=[-1/tan(T_c)]*x,x<0

y=0,x>0

y=0,T>T_c

y=[if(0,T_i>T_c)],x>0

Brewster's angle for perfect polarization by reflection (theta_i = theta_B where theta_r + theta_R=pi/2 i.e. reflected and refracted ray are perpendicular). At this angle only the component of the incident field in the plane of the interface is reflected, so the reflected ray is perfectly polarized in that plane.

180/pi*T_B

y=[-1/tan(T_B)]*x,x<0



Author: David A. Craig <http://web.lemoyne.edu/~craigda/>

Graph of the formula

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