Utilities

Contains

  • refraction_angle
  • deviation
  • lens_makers_formula
  • mirror_formula
  • lens_formula
sympy.physics.optics.utils.refraction_angle(incident, medium1, medium2, normal=None, plane=None)[source]

This function calculates transmitted vector after refraction at planar surface. medium1 and medium2 can be Medium or any sympifiable object.

If incident is an object of Ray3D, normal also has to be an instance of Ray3D in order to get the output as a Ray3D. Please note that if plane of separation is not provided and normal is an instance of Ray3D, normal will be assumed to be intersecting incident ray at the plane of separation. This will not be the case when normal is a Matrix or any other sequence. If incident is an instance of Ray3D and plane has not been provided and normal is not Ray3D, output will be a Matrix.

Parameters:

incident : Matrix, Ray3D, tuple or list

Incident vector

medium1 : sympy.physics.optics.medium.Medium or sympifiable

Medium 1 or its refractive index

medium2 : sympy.physics.optics.medium.Medium or sympifiable

Medium 2 or its refractive index

normal : Matrix, Ray3D, tuple or list

Normal vector

plane : Plane

Plane of separation of the two media.

Examples

>>> from sympy.physics.optics import refraction_angle
>>> from sympy.geometry import Point3D, Ray3D, Plane
>>> from sympy.matrices import Matrix
>>> from sympy import symbols
>>> n = Matrix([0, 0, 1])
>>> P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
>>> r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
>>> refraction_angle(r1, 1, 1, n)
Matrix([
[ 1],
[ 1],
[-1]])
>>> refraction_angle(r1, 1, 1, plane=P)
Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1))

With different index of refraction of the two media

>>> n1, n2 = symbols('n1, n2')
>>> refraction_angle(r1, n1, n2, n)
Matrix([
[                                n1/n2],
[                                n1/n2],
[-sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1)]])
>>> refraction_angle(r1, n1, n2, plane=P)
Ray3D(Point3D(0, 0, 0), Point3D(n1/n2, n1/n2, -sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1)))
sympy.physics.optics.utils.deviation(incident, medium1, medium2, normal=None, plane=None)[source]

This function calculates the angle of deviation of a ray due to refraction at planar surface.

Parameters:

incident : Matrix, Ray3D, tuple or list

Incident vector

medium1 : sympy.physics.optics.medium.Medium or sympifiable

Medium 1 or its refractive index

medium2 : sympy.physics.optics.medium.Medium or sympifiable

Medium 2 or its refractive index

normal : Matrix, Ray3D, tuple or list

Normal vector

plane : Plane

Plane of separation of the two media.

Examples

>>> from sympy.physics.optics import deviation
>>> from sympy.geometry import Point3D, Ray3D, Plane
>>> from sympy.matrices import Matrix
>>> from sympy import symbols
>>> n1, n2 = symbols('n1, n2')
>>> n = Matrix([0, 0, 1])
>>> P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
>>> r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
>>> deviation(r1, 1, 1, n)
0
>>> deviation(r1, n1, n2, plane=P)
-acos(-sqrt(-2*n1**2/(3*n2**2) + 1)) + acos(-sqrt(3)/3)
sympy.physics.optics.utils.lens_makers_formula(n_lens, n_surr, r1, r2)[source]

This function calculates focal length of a thin lens. It follows cartesian sign convention.

Parameters:

n_lens : Medium or sympifiable

Index of refraction of lens.

n_surr : Medium or sympifiable

Index of reflection of surrounding.

r1 : sympifiable

Radius of curvature of first surface.

r2 : sympifiable

Radius of curvature of second surface.

Examples

>>> from sympy.physics.optics import lens_makers_formula
>>> lens_makers_formula(1.33, 1, 10, -10)
15.1515151515151
sympy.physics.optics.utils.mirror_formula(focal_length=None, u=None, v=None)[source]

This function provides one of the three parameters when two of them are supplied. This is valid only for paraxial rays.

Parameters:

focal_length : sympifiable

Focal length of the mirror.

u : sympifiable

Distance of object from the pole on the principal axis.

v : sympifiable

Distance of the image from the pole on the principal axis.

Examples

>>> from sympy.physics.optics import mirror_formula
>>> from sympy.abc import f, u, v
>>> mirror_formula(focal_length=f, u=u)
f*u/(-f + u)
>>> mirror_formula(focal_length=f, v=v)
f*v/(-f + v)
>>> mirror_formula(u=u, v=v)
u*v/(u + v)
sympy.physics.optics.utils.lens_formula(focal_length=None, u=None, v=None)[source]

This function provides one of the three parameters when two of them are supplied. This is valid only for paraxial rays.

Parameters:

focal_length : sympifiable

Focal length of the mirror.

u : sympifiable

Distance of object from the optical center on the principal axis.

v : sympifiable

Distance of the image from the optical center on the principal axis.

Examples

>>> from sympy.physics.optics import lens_formula
>>> from sympy.abc import f, u, v
>>> lens_formula(focal_length=f, u=u)
f*u/(f + u)
>>> lens_formula(focal_length=f, v=v)
f*v/(f - v)
>>> lens_formula(u=u, v=v)
u*v/(u - v)