Added Lens formulae to the Physics repository (#10187)

* Added Lens formulae to the Physics repository

* Resolved the commented issues

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update lens_formulae.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <[email protected]>

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