Added Lens formulae to the Physics repository

physics/lens_formulae.py

@@ -0,0 +1,131 @@
+"""
+This module has functions which calculate focal length of lens, distance of
+image from the lens and distance of object from the lens.
+The above is calculated using the lens formula.
+
+In optics, the relationship between the distance of the image (v),
+the distance of the object (u), and
+the focal length (f) of the lens is given by the formula known as the Lens formula.
+The Lens formula is applicable for convex as well as concave lenses. The formula
+is given as follows:
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where
+ f = focal length of the lens in meters.
+ v = distance of the image from the lens in meters.
+ u = distance of the object from the lens in meters.
+
+To make our calculations easy few assumptions are made while deriving the formula
+which are important to keep in mind before solving this equation.
+The assumptions are as follows:
+ 1. The object O is a point object lying somewhere on the principle axis.
+ 2. The lens is thin.
+ 3. The aperture of the lens taken must be small.
+ 4. The angles of incidence and angle of refraction should be small.
+
+Sign convention is a set of rules to set signs for image distance, object distance,
+focal length, etc
+for mathematical analysis of image formation. According to it:
+ 1. Object is always placed to the left of lens.
+ 2. All distances are measured from the optical centre of the mirror.
+ 3. Distances measured in the direction of the incident ray are positive and
+ the distances measured in the direction opposite
+ to that of the incident rays are negative.
+ 4. Distances measured along y-axis above the principal axis are positive and
+ that measured along y-axis below the principal
+ axis are negative.
+
+Note: Sign convention can be reversed and will still give the correct results.
+
+Reference for Sign convention:
+https://www.toppr.com/ask/content/concept/sign-convention-for-lenses-210246/
+
+Reference for assumptions:
+https://testbook.com/physics/derivation-of-lens-maker-formula
+"""
+
+
+def focal_length_of_lens(
+ object_distance_from_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(10,4), 6.666666666666667)
+ True
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(2.7,5.8), -5.0516129032258075)
+ True
+ >>> focal_length_of_lens(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if object_distance_from_lens == 0 or image_distance_from_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ focal_length = 1 / (
+ (1 / image_distance_from_lens) - (1 / object_distance_from_lens)
+ )
+ return focal_length
+
+
+def object_distance(
+ focal_length_of_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(object_distance(10,40), -13.333333333333332)
+ True
+
+ >>> from math import isclose
+ >>> isclose(object_distance(6.2,1.5), 1.9787234042553192)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if image_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+
+ object_distance = 1 / ((1 / image_distance_from_lens) - (1 / focal_length_of_lens))
+ return object_distance
+
+
+def image_distance(
+ focal_length_of_lens: float, object_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(image_distance(50,40), 22.22222222222222)
+ True
+ >>> from math import isclose
+ >>> isclose(image_distance(5.3,7.9), 3.1719696969696973)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+ if object_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ image_distance = 1 / ((1 / object_distance_from_lens) + (1 / focal_length_of_lens))
+ return image_distance

physics/lens_formulae.py

@@ -0,0 +1,131 @@
+"""
+This module has functions which calculate focal length of lens, distance of
+image from the lens and distance of object from the lens.
+The above is calculated using the lens formula.
+
+In optics, the relationship between the distance of the image (v),
+the distance of the object (u), and
+the focal length (f) of the lens is given by the formula known as the Lens formula.
+The Lens formula is applicable for convex as well as concave lenses. The formula
+is given as follows:
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where
+ f = focal length of the lens in meters.
+ v = distance of the image from the lens in meters.
+ u = distance of the object from the lens in meters.
+
+To make our calculations easy few assumptions are made while deriving the formula
+which are important to keep in mind before solving this equation.
+The assumptions are as follows:
+ 1. The object O is a point object lying somewhere on the principle axis.
+ 2. The lens is thin.
+ 3. The aperture of the lens taken must be small.
+ 4. The angles of incidence and angle of refraction should be small.
+
+Sign convention is a set of rules to set signs for image distance, object distance,
+focal length, etc
+for mathematical analysis of image formation. According to it:
+ 1. Object is always placed to the left of lens.
+ 2. All distances are measured from the optical centre of the mirror.
+ 3. Distances measured in the direction of the incident ray are positive and
+ the distances measured in the direction opposite
+ to that of the incident rays are negative.
+ 4. Distances measured along y-axis above the principal axis are positive and
+ that measured along y-axis below the principal
+ axis are negative.
+
+Note: Sign convention can be reversed and will still give the correct results.
+
+Reference for Sign convention:
+https://www.toppr.com/ask/content/concept/sign-convention-for-lenses-210246/
+
+Reference for assumptions:
+https://testbook.com/physics/derivation-of-lens-maker-formula
+"""
+
+
+def focal_length_of_lens(
+ object_distance_from_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(10,4), 6.666666666666667)
+ True
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(2.7,5.8), -5.0516129032258075)
+ True
+ >>> focal_length_of_lens(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if object_distance_from_lens == 0 or image_distance_from_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ focal_length = 1 / (
+ (1 / image_distance_from_lens) - (1 / object_distance_from_lens)
+ )
+ return focal_length
+
+
+def object_distance(
+ focal_length_of_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(object_distance(10,40), -13.333333333333332)
+ True
+
+ >>> from math import isclose
+ >>> isclose(object_distance(6.2,1.5), 1.9787234042553192)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if image_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+
+ object_distance = 1 / ((1 / image_distance_from_lens) - (1 / focal_length_of_lens))
+ return object_distance
+
+
+def image_distance(
+ focal_length_of_lens: float, object_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(image_distance(50,40), 22.22222222222222)
+ True
+ >>> from math import isclose
+ >>> isclose(image_distance(5.3,7.9), 3.1719696969696973)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+ if object_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ image_distance = 1 / ((1 / object_distance_from_lens) + (1 / focal_length_of_lens))
+ return image_distance

physics/lens_formulae.py

@@ -0,0 +1,131 @@
+"""
+This module has functions which calculate focal length of lens, distance of
+image from the lens and distance of object from the lens.
+The above is calculated using the lens formula.
+
+In optics, the relationship between the distance of the image (v),
+the distance of the object (u), and
+the focal length (f) of the lens is given by the formula known as the Lens formula.
+The Lens formula is applicable for convex as well as concave lenses. The formula
+is given as follows:
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where
+ f = focal length of the lens in meters.
+ v = distance of the image from the lens in meters.
+ u = distance of the object from the lens in meters.
+
+To make our calculations easy few assumptions are made while deriving the formula
+which are important to keep in mind before solving this equation.
+The assumptions are as follows:
+ 1. The object O is a point object lying somewhere on the principle axis.
+ 2. The lens is thin.
+ 3. The aperture of the lens taken must be small.
+ 4. The angles of incidence and angle of refraction should be small.
+
+Sign convention is a set of rules to set signs for image distance, object distance,
+focal length, etc
+for mathematical analysis of image formation. According to it:
+ 1. Object is always placed to the left of lens.
+ 2. All distances are measured from the optical centre of the mirror.
+ 3. Distances measured in the direction of the incident ray are positive and
+ the distances measured in the direction opposite
+ to that of the incident rays are negative.
+ 4. Distances measured along y-axis above the principal axis are positive and
+ that measured along y-axis below the principal
+ axis are negative.
+
+Note: Sign convention can be reversed and will still give the correct results.
+
+Reference for Sign convention:
+https://www.toppr.com/ask/content/concept/sign-convention-for-lenses-210246/
+
+Reference for assumptions:
+https://testbook.com/physics/derivation-of-lens-maker-formula
+"""
+
+
+def focal_length_of_lens(
+ object_distance_from_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(10,4), 6.666666666666667)
+ True
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(2.7,5.8), -5.0516129032258075)
+ True
+ >>> focal_length_of_lens(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if object_distance_from_lens == 0 or image_distance_from_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ focal_length = 1 / (
+ (1 / image_distance_from_lens) - (1 / object_distance_from_lens)
+ )
+ return focal_length
+
+
+def object_distance(
+ focal_length_of_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(object_distance(10,40), -13.333333333333332)
+ True
+
+ >>> from math import isclose
+ >>> isclose(object_distance(6.2,1.5), 1.9787234042553192)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if image_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+
+ object_distance = 1 / ((1 / image_distance_from_lens) - (1 / focal_length_of_lens))
+ return object_distance
+
+
+def image_distance(
+ focal_length_of_lens: float, object_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(image_distance(50,40), 22.22222222222222)
+ True
+ >>> from math import isclose
+ >>> isclose(image_distance(5.3,7.9), 3.1719696969696973)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+ if object_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ image_distance = 1 / ((1 / object_distance_from_lens) + (1 / focal_length_of_lens))
+ return image_distance

physics/lens_formulae.py

@@ -0,0 +1,131 @@
+"""
+This module has functions which calculate focal length of lens, distance of
+image from the lens and distance of object from the lens.
+The above is calculated using the lens formula.
+
+In optics, the relationship between the distance of the image (v),
+the distance of the object (u), and
+the focal length (f) of the lens is given by the formula known as the Lens formula.
+The Lens formula is applicable for convex as well as concave lenses. The formula
+is given as follows:
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where
+ f = focal length of the lens in meters.
+ v = distance of the image from the lens in meters.
+ u = distance of the object from the lens in meters.
+
+To make our calculations easy few assumptions are made while deriving the formula
+which are important to keep in mind before solving this equation.
+The assumptions are as follows:
+ 1. The object O is a point object lying somewhere on the principle axis.
+ 2. The lens is thin.
+ 3. The aperture of the lens taken must be small.
+ 4. The angles of incidence and angle of refraction should be small.
+
+Sign convention is a set of rules to set signs for image distance, object distance,
+focal length, etc
+for mathematical analysis of image formation. According to it:
+ 1. Object is always placed to the left of lens.
+ 2. All distances are measured from the optical centre of the mirror.
+ 3. Distances measured in the direction of the incident ray are positive and
+ the distances measured in the direction opposite
+ to that of the incident rays are negative.
+ 4. Distances measured along y-axis above the principal axis are positive and
+ that measured along y-axis below the principal
+ axis are negative.
+
+Note: Sign convention can be reversed and will still give the correct results.
+
+Reference for Sign convention:
+https://www.toppr.com/ask/content/concept/sign-convention-for-lenses-210246/
+
+Reference for assumptions:
+https://testbook.com/physics/derivation-of-lens-maker-formula
+"""
+
+
+def focal_length_of_lens(
+ object_distance_from_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(10,4), 6.666666666666667)
+ True
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(2.7,5.8), -5.0516129032258075)
+ True
+ >>> focal_length_of_lens(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if object_distance_from_lens == 0 or image_distance_from_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ focal_length = 1 / (
+ (1 / image_distance_from_lens) - (1 / object_distance_from_lens)
+ )
+ return focal_length
+
+
+def object_distance(
+ focal_length_of_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(object_distance(10,40), -13.333333333333332)
+ True
+
+ >>> from math import isclose
+ >>> isclose(object_distance(6.2,1.5), 1.9787234042553192)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if image_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+
+ object_distance = 1 / ((1 / image_distance_from_lens) - (1 / focal_length_of_lens))
+ return object_distance
+
+
+def image_distance(
+ focal_length_of_lens: float, object_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(image_distance(50,40), 22.22222222222222)
+ True
+ >>> from math import isclose
+ >>> isclose(image_distance(5.3,7.9), 3.1719696969696973)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+ if object_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ image_distance = 1 / ((1 / object_distance_from_lens) + (1 / focal_length_of_lens))
+ return image_distance

physics/lens_formulae.py

@@ -0,0 +1,131 @@
+"""
+This module has functions which calculate focal length of lens, distance of
+image from the lens and distance of object from the lens.
+The above is calculated using the lens formula.
+
+In optics, the relationship between the distance of the image (v),
+the distance of the object (u), and
+the focal length (f) of the lens is given by the formula known as the Lens formula.
+The Lens formula is applicable for convex as well as concave lenses. The formula
+is given as follows:
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where
+ f = focal length of the lens in meters.
+ v = distance of the image from the lens in meters.
+ u = distance of the object from the lens in meters.
+
+To make our calculations easy few assumptions are made while deriving the formula
+which are important to keep in mind before solving this equation.
+The assumptions are as follows:
+ 1. The object O is a point object lying somewhere on the principle axis.
+ 2. The lens is thin.
+ 3. The aperture of the lens taken must be small.
+ 4. The angles of incidence and angle of refraction should be small.
+
+Sign convention is a set of rules to set signs for image distance, object distance,
+focal length, etc
+for mathematical analysis of image formation. According to it:
+ 1. Object is always placed to the left of lens.
+ 2. All distances are measured from the optical centre of the mirror.
+ 3. Distances measured in the direction of the incident ray are positive and
+ the distances measured in the direction opposite
+ to that of the incident rays are negative.
+ 4. Distances measured along y-axis above the principal axis are positive and
+ that measured along y-axis below the principal
+ axis are negative.
+
+Note: Sign convention can be reversed and will still give the correct results.
+
+Reference for Sign convention:
+https://www.toppr.com/ask/content/concept/sign-convention-for-lenses-210246/
+
+Reference for assumptions:
+https://testbook.com/physics/derivation-of-lens-maker-formula
+"""
+
+
+def focal_length_of_lens(
+ object_distance_from_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(10,4), 6.666666666666667)
+ True
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(2.7,5.8), -5.0516129032258075)
+ True
+ >>> focal_length_of_lens(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if object_distance_from_lens == 0 or image_distance_from_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ focal_length = 1 / (
+ (1 / image_distance_from_lens) - (1 / object_distance_from_lens)
+ )
+ return focal_length
+
+
+def object_distance(
+ focal_length_of_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(object_distance(10,40), -13.333333333333332)
+ True
+
+ >>> from math import isclose
+ >>> isclose(object_distance(6.2,1.5), 1.9787234042553192)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if image_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+
+ object_distance = 1 / ((1 / image_distance_from_lens) - (1 / focal_length_of_lens))
+ return object_distance
+
+
+def image_distance(
+ focal_length_of_lens: float, object_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(image_distance(50,40), 22.22222222222222)
+ True
+ >>> from math import isclose
+ >>> isclose(image_distance(5.3,7.9), 3.1719696969696973)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+ if object_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ image_distance = 1 / ((1 / object_distance_from_lens) + (1 / focal_length_of_lens))
+ return image_distance

physics/lens_formulae.py

@@ -0,0 +1,131 @@
+"""
+This module has functions which calculate focal length of lens, distance of
+image from the lens and distance of object from the lens.
+The above is calculated using the lens formula.
+
+In optics, the relationship between the distance of the image (v),
+the distance of the object (u), and
+the focal length (f) of the lens is given by the formula known as the Lens formula.
+The Lens formula is applicable for convex as well as concave lenses. The formula
+is given as follows:
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where
+ f = focal length of the lens in meters.
+ v = distance of the image from the lens in meters.
+ u = distance of the object from the lens in meters.
+
+To make our calculations easy few assumptions are made while deriving the formula
+which are important to keep in mind before solving this equation.
+The assumptions are as follows:
+ 1. The object O is a point object lying somewhere on the principle axis.
+ 2. The lens is thin.
+ 3. The aperture of the lens taken must be small.
+ 4. The angles of incidence and angle of refraction should be small.
+
+Sign convention is a set of rules to set signs for image distance, object distance,
+focal length, etc
+for mathematical analysis of image formation. According to it:
+ 1. Object is always placed to the left of lens.
+ 2. All distances are measured from the optical centre of the mirror.
+ 3. Distances measured in the direction of the incident ray are positive and
+ the distances measured in the direction opposite
+ to that of the incident rays are negative.
+ 4. Distances measured along y-axis above the principal axis are positive and
+ that measured along y-axis below the principal
+ axis are negative.
+
+Note: Sign convention can be reversed and will still give the correct results.
+
+Reference for Sign convention:
+https://www.toppr.com/ask/content/concept/sign-convention-for-lenses-210246/
+
+Reference for assumptions:
+https://testbook.com/physics/derivation-of-lens-maker-formula
+"""
+
+
+def focal_length_of_lens(
+ object_distance_from_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(10,4), 6.666666666666667)
+ True
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(2.7,5.8), -5.0516129032258075)
+ True
+ >>> focal_length_of_lens(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if object_distance_from_lens == 0 or image_distance_from_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ focal_length = 1 / (
+ (1 / image_distance_from_lens) - (1 / object_distance_from_lens)
+ )
+ return focal_length
+
+
+def object_distance(
+ focal_length_of_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(object_distance(10,40), -13.333333333333332)
+ True
+
+ >>> from math import isclose
+ >>> isclose(object_distance(6.2,1.5), 1.9787234042553192)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if image_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+
+ object_distance = 1 / ((1 / image_distance_from_lens) - (1 / focal_length_of_lens))
+ return object_distance
+
+
+def image_distance(
+ focal_length_of_lens: float, object_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(image_distance(50,40), 22.22222222222222)
+ True
+ >>> from math import isclose
+ >>> isclose(image_distance(5.3,7.9), 3.1719696969696973)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+ if object_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ image_distance = 1 / ((1 / object_distance_from_lens) + (1 / focal_length_of_lens))
+ return image_distance

physics/lens_formulae.py

@@ -0,0 +1,131 @@
+"""
+This module has functions which calculate focal length of lens, distance of
+image from the lens and distance of object from the lens.
+The above is calculated using the lens formula.
+
+In optics, the relationship between the distance of the image (v),
+the distance of the object (u), and
+the focal length (f) of the lens is given by the formula known as the Lens formula.
+The Lens formula is applicable for convex as well as concave lenses. The formula
+is given as follows:
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where
+ f = focal length of the lens in meters.
+ v = distance of the image from the lens in meters.
+ u = distance of the object from the lens in meters.
+
+To make our calculations easy few assumptions are made while deriving the formula
+which are important to keep in mind before solving this equation.
+The assumptions are as follows:
+ 1. The object O is a point object lying somewhere on the principle axis.
+ 2. The lens is thin.
+ 3. The aperture of the lens taken must be small.
+ 4. The angles of incidence and angle of refraction should be small.
+
+Sign convention is a set of rules to set signs for image distance, object distance,
+focal length, etc
+for mathematical analysis of image formation. According to it:
+ 1. Object is always placed to the left of lens.
+ 2. All distances are measured from the optical centre of the mirror.
+ 3. Distances measured in the direction of the incident ray are positive and
+ the distances measured in the direction opposite
+ to that of the incident rays are negative.
+ 4. Distances measured along y-axis above the principal axis are positive and
+ that measured along y-axis below the principal
+ axis are negative.
+
+Note: Sign convention can be reversed and will still give the correct results.
+
+Reference for Sign convention:
+https://www.toppr.com/ask/content/concept/sign-convention-for-lenses-210246/
+
+Reference for assumptions:
+https://testbook.com/physics/derivation-of-lens-maker-formula
+"""
+
+
+def focal_length_of_lens(
+ object_distance_from_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(10,4), 6.666666666666667)
+ True
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(2.7,5.8), -5.0516129032258075)
+ True
+ >>> focal_length_of_lens(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if object_distance_from_lens == 0 or image_distance_from_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ focal_length = 1 / (
+ (1 / image_distance_from_lens) - (1 / object_distance_from_lens)
+ )
+ return focal_length
+
+
+def object_distance(
+ focal_length_of_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(object_distance(10,40), -13.333333333333332)
+ True
+
+ >>> from math import isclose
+ >>> isclose(object_distance(6.2,1.5), 1.9787234042553192)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if image_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+
+ object_distance = 1 / ((1 / image_distance_from_lens) - (1 / focal_length_of_lens))
+ return object_distance
+
+
+def image_distance(
+ focal_length_of_lens: float, object_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(image_distance(50,40), 22.22222222222222)
+ True
+ >>> from math import isclose
+ >>> isclose(image_distance(5.3,7.9), 3.1719696969696973)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+ if object_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ image_distance = 1 / ((1 / object_distance_from_lens) + (1 / focal_length_of_lens))
+ return image_distance

physics/lens_formulae.py

@@ -0,0 +1,131 @@
+"""
+This module has functions which calculate focal length of lens, distance of
+image from the lens and distance of object from the lens.
+The above is calculated using the lens formula.
+
+In optics, the relationship between the distance of the image (v),
+the distance of the object (u), and
+the focal length (f) of the lens is given by the formula known as the Lens formula.
+The Lens formula is applicable for convex as well as concave lenses. The formula
+is given as follows:
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where
+ f = focal length of the lens in meters.
+ v = distance of the image from the lens in meters.
+ u = distance of the object from the lens in meters.
+
+To make our calculations easy few assumptions are made while deriving the formula
+which are important to keep in mind before solving this equation.
+The assumptions are as follows:
+ 1. The object O is a point object lying somewhere on the principle axis.
+ 2. The lens is thin.
+ 3. The aperture of the lens taken must be small.
+ 4. The angles of incidence and angle of refraction should be small.
+
+Sign convention is a set of rules to set signs for image distance, object distance,
+focal length, etc
+for mathematical analysis of image formation. According to it:
+ 1. Object is always placed to the left of lens.
+ 2. All distances are measured from the optical centre of the mirror.
+ 3. Distances measured in the direction of the incident ray are positive and
+ the distances measured in the direction opposite
+ to that of the incident rays are negative.
+ 4. Distances measured along y-axis above the principal axis are positive and
+ that measured along y-axis below the principal
+ axis are negative.
+
+Note: Sign convention can be reversed and will still give the correct results.
+
+Reference for Sign convention:
+https://www.toppr.com/ask/content/concept/sign-convention-for-lenses-210246/
+
+Reference for assumptions:
+https://testbook.com/physics/derivation-of-lens-maker-formula
+"""
+
+
+def focal_length_of_lens(
+ object_distance_from_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(10,4), 6.666666666666667)
+ True
+ >>> from math import isclose
+ >>> isclose(focal_length_of_lens(2.7,5.8), -5.0516129032258075)
+ True
+ >>> focal_length_of_lens(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if object_distance_from_lens == 0 or image_distance_from_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ focal_length = 1 / (
+ (1 / image_distance_from_lens) - (1 / object_distance_from_lens)
+ )
+ return focal_length
+
+
+def object_distance(
+ focal_length_of_lens: float, image_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(object_distance(10,40), -13.333333333333332)
+ True
+
+ >>> from math import isclose
+ >>> isclose(object_distance(6.2,1.5), 1.9787234042553192)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+
+ if image_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+
+ object_distance = 1 / ((1 / image_distance_from_lens) - (1 / focal_length_of_lens))
+ return object_distance
+
+
+def image_distance(
+ focal_length_of_lens: float, object_distance_from_lens: float
+) -> float:
+ """
+ Doctests:
+ >>> from math import isclose
+ >>> isclose(image_distance(50,40), 22.22222222222222)
+ True
+ >>> from math import isclose
+ >>> isclose(image_distance(5.3,7.9), 3.1719696969696973)
+ True
+
+ >>> object_distance(0, 20) # doctest: +NORMALIZE_WHITESPACE
+ Traceback (most recent call last):
+ ...
+ ValueError: Invalid inputs. Enter non zero values with respect
+ to the sign convention.
+ """
+ if object_distance_from_lens == 0 or focal_length_of_lens == 0:
+ raise ValueError(
+ "Invalid inputs. Enter non zero values with respect to the sign convention."
+ )
+ image_distance = 1 / ((1 / object_distance_from_lens) + (1 / focal_length_of_lens))
+ return image_distance