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import numpy as np
import pylab
import sys
def drawPrismDisk(prismAngleInDegrees, nDisk, nPrism, diskX, coupDesc):
# Calculates incident angle for proper coupling into the disc via prism
# prismAngleInDegrees - angle of the prism faces in degrees
# diskX - x coordinate of the disk center
# coupDesc - short annotation of the situation
prismAngle = prismAngleInDegrees * np.pi / 180 # convert to radians
# critical angle for beam from prism to disk. we want thetaDisk to be 90
# degrees, i.e. total internal reflection -> sin(thetaDisk) = 1.0
thetaPrism1 = np.arcsin(nDisk / nPrism)
thetaPrismInDegrees1 = thetaPrism1 * 180 / np.pi
# find inside angle on the incident side of prism
thetaPrism2 = prismAngle - thetaPrism1
thetaPrismInDegrees2 = thetaPrism2 * 180 / np.pi #convert to degrees
# calculate refracted angle out of the prism with respect to the normal
# positive means above the normal; negative below
tempArcsin = nPrism * np.sin(thetaPrism2)
try:
thetaAir = np.arcsin(tempArcsin)
except ValueError:
print 'Error'
sys.exit('Total internal reflection at right prism face')
thetaAir = np.arcsin(tempArcsin)
thetaAirInDegrees = thetaAir * 180 / np.pi #convert to degrees
# angle in the air relative to horizon
thetaAirHorizon = thetaAir + (np.pi/2 - prismAngle)
thetaAirHorizonInDegrees = thetaAirHorizon * 180 / np.pi #convert to degrees
# -----GRAPHICAL OUTPUT-----
# PRISM
# bottom face will go from (-1,0) to (1,0) regardless of prismAngle
xFace1 = np.linspace(-1,1)
yFace1 = 0 * xFace1
# second face to the right of origin
# at prismAngle with respect to negative x-direction
xFace2 = np.linspace(1,0)
yFace2 = (1 - xFace2) * np.tan(prismAngle)
# third face to the left of origin
# at prismAngle with respect to positive x-direction
xFace3 = np.linspace(-1,0)
yFace3 = (xFace3 + 1) * np.tan(prismAngle)
# draw prism
pylab.plot(xFace1, yFace1, 'black',\
xFace2, yFace2, 'black',\
xFace3, yFace3, 'black')
# BEAMS
# Inside Prism
# drawing line from disk contact point to face2 at angle thetaPrism
xCross = (np.tan(prismAngle) + diskX / np.tan(thetaPrism1)) /\
(1/np.tan(thetaPrism1) + np.tan(prismAngle))
yCross = -np.tan(prismAngle) * (xCross - 1)
xBeamPrism = np.linspace(diskX, xCross)
yBeamPrism = np.linspace(0, yCross)
pylab.plot(xBeamPrism, yBeamPrism, color = 'red', linewidth = 2)
# Outside Prism
xOutStart = xCross
yOutStart = yCross
xOutStop = 1.5
xBeamOut = np.linspace(xOutStart, xOutStop)
yBeamOut = yOutStart + np.tan(thetaAirHorizon) * (xBeamOut - xOutStart)
# this keeps the beam from going farther than necessary
i = 0
for value in yBeamOut:
if value > 2.0:
break
else:
i +=1
# ensure same dimension
yBeamOut = yBeamOut[:i]
xBeamOut = xBeamOut[:i]
pylab.plot(xBeamOut, yBeamOut, color = 'red', linewidth = 2)
# General annotation and axis set-up
pylab.text(-1.4, 1.7, coupDesc)
pylab.text(-1.4, 1.55, 'nDisk = %.3f' % nDisk)
pylab.text(-1.4, 1.4, 'nPrism = %.3f' % nPrism)
pylab.xlim(-1.5, 1.5)
pylab.ylim(-0.5, 2.0)
pylab.title(coupDesc)
return [xBeamOut[-1], yBeamOut[-1], yFace2[-1], yFace3[-1],\
thetaPrism1, thetaPrism2, thetaAirHorizon]
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