return ampl * sin(k * r) / sqrt(r)
ndiv = 100
ampl = 1.
lmbd = 1.
k = 2. * pi / lmbd
d = 50.
a = 2.
yl = -50.
yr = 50.
ny = 100
hy = (yr - yl) / ny
yarr = []
iarr = []
for iy in range(0, ny - 1):
y = yl + iy * hy
i = simpson(-a / 2., a / 2., ndiv, real_amp) ** 2 + simpson(-a / 2, a / 2, ndiv, imag_amp) ** 2
yarr.append(180 / pi * asin(y / sqrt(y ** 2 + d ** 2)))
iarr.append(i)
pyplot.figure('Exercise 1 - intensity chart', figsize=(9.5, 7))
pyplot.title('Intensity chart\nParameters: λ = %.2f, a = %.2f, d = %.2f' % (lmbd, a, d))
pyplot.xlabel("Angle from the system's axis of symmetry")
pyplot.ylabel('Intensity')
pyplot.plot(yarr, iarr)
pyplot.show()
numberOfSlits = 2
slitWidth = 10.
distanceBetweenSlits = 8
yarr = []
iarr = []
xrMAX = 0.5 * (numberOfSlits * slitWidth +
(numberOfSlits - 1) * distanceBetweenSlits)
for iy in range(0, ny - 1):
y = yl + iy * hy
intensity = 0
xl = -0.5 * (numberOfSlits * slitWidth +
(numberOfSlits - 1) * distanceBetweenSlits)
xr = xl + slitWidth
while xr <= xrMAX:
intensity += simpson(xl, xr, ndiv, real_amp)**2 + simpson(
xl, xr, ndiv, imag_amp)**2
xl += slitWidth + distanceBetweenSlits
xr = xl + slitWidth
yarr.append(180 / pi * asin(y / sqrt(y**2 + d**2)))
iarr.append(intensity)
pyplot.figure('Multi-slit chart', figsize=(9.5, 7))
pyplot.title(
'Intensity of wave\nParameters: λ = %.2f, a = %.2f, number of slits= %.2f, distance between slits = %.2f'
% (lmbd, slitWidth, numberOfSlits, distanceBetweenSlits))
pyplot.xlabel("Angle from the system's axis of symmetry")
pyplot.ylabel('Intensity')
pyplot.plot(yarr, iarr)
pyplot.show()
import matplotlib.pyplot as plt
import time
xl = 0
xr = 1
logValues = []
simpsonValues = []
calcTimes = []
nMax = floor(log10(1000000000))
for i in range(1, nMax):
N = 10**i
h = (xr - xl) / N / 2
logValues.append(-log10(h))
start = time.time()
simpsonValues.append(simpson(xl, xr, N, fun))
end = time.time()
calcTimes.append(end - start)
plt.plot(logValues, simpsonValues)
plt.grid(1)
plt.title("Nf = " + str(N))
plt.xlabel("-log(h)")
plt.ylim([0, 2])
plt.ylabel("F")
plt.show()
plt.plot(logValues, calcTimes)
plt.grid(1)
plt.title("Nf = " + str(N))
plt.xlabel("-log(h)")
plt.ylabel("t [s]")
slitWidth = 10.
distanceBetweenSlits = 8.
yarr = []
iarr = []
xrMAX = 0.5 * (numberOfSlits * slitWidth +
(numberOfSlits - 1) * distanceBetweenSlits)
for iy in range(0, ny - 1):
y = yl + iy * hy
intensityRe = 0
intensityIm = 0
xl = -0.5 * (numberOfSlits * slitWidth +
(numberOfSlits - 1) * distanceBetweenSlits)
xr = xl + slitWidth
while xr <= xrMAX:
intensityRe += simpson(xl, xr, ndiv, real_amp)
intensityIm += simpson(xl, xr, ndiv, imag_amp)
xl += slitWidth + distanceBetweenSlits
xr = xl + slitWidth
yarr.append(180 / pi * asin(y / sqrt(y**2 + d**2)))
intensity = intensityRe**2 + intensityIm**2
iarr.append(intensity)
pyplot.figure('Multi-slit chart', figsize=(9.5, 7))
pyplot.title(
'Intensity of wave\nParameters: λ = %.2f, a = %.2f, number of slits= %.2f, distance between slits = %.2f'
% (lmbd, slitWidth, numberOfSlits, distanceBetweenSlits))
pyplot.xlabel("Angle from the system's axis of symmetry")
pyplot.ylabel('Intensity')
pyplot.plot(yarr, iarr)
pyplot.show()
from quadrat import simpson
from math import sqrt, log
import matplotlib.pyplot as plt
def fun(x):
return 4 * sqrt(1 - x * x)
print(simpson(0, 1, 1000000, fun))