Added Mirror Formulae Equation (#9717)

* Python mirror_formulae.py is added to the repository

* Changes done after reading readme.md

* Changes for running doctest on all platforms

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

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* Change 2 for Doctests

* Changes for doctest 2

* updating DIRECTORY.md

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DIRECTORY.md

@@ -170,6 +170,7 @@
 
 ## Data Structures
   * Arrays
+    * [Median Two Array](data_structures/arrays/median_two_array.py)
     * [Permutations](data_structures/arrays/permutations.py)
     * [Prefix Sum](data_structures/arrays/prefix_sum.py)
     * [Product Sum](data_structures/arrays/product_sum.py)
@@ -185,6 +186,7 @@
     * [Diff Views Of Binary Tree](data_structures/binary_tree/diff_views_of_binary_tree.py)
     * [Distribute Coins](data_structures/binary_tree/distribute_coins.py)
     * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py)
+    * [Flatten Binarytree To Linkedlist](data_structures/binary_tree/flatten_binarytree_to_linkedlist.py)
     * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py)
     * [Is Bst](data_structures/binary_tree/is_bst.py)
     * [Lazy Segment Tree](data_structures/binary_tree/lazy_segment_tree.py)
@@ -324,6 +326,7 @@
   * [Longest Common Substring](dynamic_programming/longest_common_substring.py)
   * [Longest Increasing Subsequence](dynamic_programming/longest_increasing_subsequence.py)
   * [Longest Increasing Subsequence O(Nlogn)](dynamic_programming/longest_increasing_subsequence_o(nlogn).py)
+  * [Longest Palindromic Subsequence](dynamic_programming/longest_palindromic_subsequence.py)
   * [Longest Sub Array](dynamic_programming/longest_sub_array.py)
   * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py)
   * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py)
@@ -539,6 +542,7 @@
   * [Average Mode](maths/average_mode.py)
   * [Bailey Borwein Plouffe](maths/bailey_borwein_plouffe.py)
   * [Basic Maths](maths/basic_maths.py)
+  * [Bell Numbers](maths/bell_numbers.py)
   * [Binary Exp Mod](maths/binary_exp_mod.py)
   * [Binary Exponentiation](maths/binary_exponentiation.py)
   * [Binary Exponentiation 3](maths/binary_exponentiation_3.py)
@@ -690,6 +694,7 @@
   * [Matrix Class](matrix/matrix_class.py)
   * [Matrix Operation](matrix/matrix_operation.py)
   * [Max Area Of Island](matrix/max_area_of_island.py)
+  * [Median Matrix](matrix/median_matrix.py)
   * [Nth Fibonacci Using Matrix Exponentiation](matrix/nth_fibonacci_using_matrix_exponentiation.py)
   * [Pascal Triangle](matrix/pascal_triangle.py)
   * [Rotate Matrix](matrix/rotate_matrix.py)
@@ -708,8 +713,8 @@
   * Activation Functions
     * [Exponential Linear Unit](neural_network/activation_functions/exponential_linear_unit.py)
     * [Leaky Rectified Linear Unit](neural_network/activation_functions/leaky_rectified_linear_unit.py)
-    * [Scaled Exponential Linear Unit](neural_network/activation_functions/scaled_exponential_linear_unit.py)
     * [Rectified Linear Unit](neural_network/activation_functions/rectified_linear_unit.py)
+    * [Scaled Exponential Linear Unit](neural_network/activation_functions/scaled_exponential_linear_unit.py)
   * [Back Propagation Neural Network](neural_network/back_propagation_neural_network.py)
   * [Convolution Neural Network](neural_network/convolution_neural_network.py)
   * [Perceptron](neural_network/perceptron.py)
@@ -756,9 +761,11 @@
   * [Kinetic Energy](physics/kinetic_energy.py)
   * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py)
   * [Malus Law](physics/malus_law.py)
+  * [Mirror Formulae](physics/mirror_formulae.py)
   * [N Body Simulation](physics/n_body_simulation.py)
   * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py)
   * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py)
+  * [Photoelectric Effect](physics/photoelectric_effect.py)
   * [Potential Energy](physics/potential_energy.py)
   * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py)
   * [Shear Stress](physics/shear_stress.py)

physics/mirror_formulae.py

@@ -0,0 +1,127 @@
+"""
+This module contains the functions to calculate the focal length, object distance
+and image distance of a mirror.
+
+The mirror formula is an equation that relates the object distance (u),
+image distance (v), and focal length (f) of a spherical mirror.
+It is commonly used in optics to determine the position and characteristics
+of an image formed by a mirror. It is expressed using the formulae :
+
+-------------------
+| 1/f = 1/v + 1/u |
+-------------------
+
+Where,
+f = Focal length of the spherical mirror (metre)
+v = Image distance from the mirror (metre)
+u = Object distance from the mirror (metre)
+
+
+The signs of the distances are taken with respect to the sign convention.
+The sign convention is as follows:
+    1) Object is always placed to the left of mirror
+    2) 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.
+    3) All distances are measured from the pole of the mirror.
+
+
+There are a few assumptions that are made while using the mirror formulae.
+They are as follows:
+    1) Thin Mirror: The mirror is assumed to be thin, meaning its thickness is
+    negligible compared to its radius of curvature. This assumption allows
+    us to treat the mirror as a two-dimensional surface.
+    2) Spherical Mirror: The mirror is assumed to have a spherical shape. While this
+    assumption may not hold exactly for all mirrors, it is a reasonable approximation
+    for most practical purposes.
+    3) Small Angles: The angles involved in the derivation are assumed to be small.
+    This assumption allows us to use the small-angle approximation, where the tangent
+    of a small angle is approximately equal to the angle itself. It simplifies the
+    calculations and makes the derivation more manageable.
+    4) Paraxial Rays: The mirror formula is derived using paraxial rays, which are
+    rays that are close to the principal axis and make small angles with it. This
+    assumption ensures that the rays are close enough to the principal axis, making the
+    calculations more accurate.
+    5) Reflection and Refraction Laws: The derivation assumes that the laws of
+    reflection and refraction hold.
+    These laws state that the angle of incidence is equal to the angle of reflection
+    for reflection, and the incident and refracted rays lie in the same plane and
+    obey Snell's law for refraction.
+
+(Description and Assumptions adapted from
+https://www.collegesearch.in/articles/mirror-formula-derivation)
+
+(Sign Convention adapted from
+https://www.toppr.com/ask/content/concept/sign-convention-for-mirrors-210189/)
+
+
+"""
+
+
+def focal_length(distance_of_object: float, distance_of_image: float) -> float:
+    """
+    >>> from math import isclose
+    >>> isclose(focal_length(10, 20), 6.66666666666666)
+    True
+    >>> from math import isclose
+    >>> isclose(focal_length(9.5, 6.7), 3.929012346)
+    True
+    >>> focal_length(0, 20)
+    Traceback (most recent call last):
+        ...
+    ValueError: Invalid inputs. Enter non zero values with respect
+    to the sign convention.
+    """
+
+    if distance_of_object == 0 or distance_of_image == 0:
+        raise ValueError(
+            "Invalid inputs. Enter non zero values with respect to the sign convention."
+        )
+    focal_length = 1 / ((1 / distance_of_object) + (1 / distance_of_image))
+    return focal_length
+
+
+def object_distance(focal_length: float, distance_of_image: float) -> float:
+    """
+    >>> from math import isclose
+    >>> isclose(object_distance(30, 20), -60.0)
+    True
+    >>> from math import isclose
+    >>> isclose(object_distance(10.5, 11.7), 102.375)
+    True
+    >>> object_distance(90, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: Invalid inputs. Enter non zero values with respect
+    to the sign convention.
+    """
+
+    if distance_of_image == 0 or focal_length == 0:
+        raise ValueError(
+            "Invalid inputs. Enter non zero values with respect to the sign convention."
+        )
+    object_distance = 1 / ((1 / focal_length) - (1 / distance_of_image))
+    return object_distance
+
+
+def image_distance(focal_length: float, distance_of_object: float) -> float:
+    """
+    >>> from math import isclose
+    >>> isclose(image_distance(10, 40), 13.33333333)
+    True
+    >>> from math import isclose
+    >>> isclose(image_distance(1.5, 6.7), 1.932692308)
+    True
+    >>> image_distance(0, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: Invalid inputs. Enter non zero values with respect
+    to the sign convention.
+    """
+
+    if distance_of_object == 0 or focal_length == 0:
+        raise ValueError(
+            "Invalid inputs. Enter non zero values with respect to the sign convention."
+        )
+    image_distance = 1 / ((1 / focal_length) - (1 / distance_of_object))
+    return image_distance