Added Mirror Formulae Equation #9717
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| """ | ||
| This module contains the functions to calculate the focal length, object distance | ||
| and image distance of a mirror. | ||
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| 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 : | ||
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| ------------------- | ||
| | 1/f = 1/v + 1/u | | ||
| ------------------- | ||
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| Where, | ||
| f = Focal length of the spherical mirror (metre) | ||
| v = Image distance from the mirror (metre) | ||
| u = Object distance from the mirror (metre) | ||
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| 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. | ||
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| 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. | ||
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| (Description and Assumptions adapted from | ||
| https://www.collegesearch.in/articles/mirror-formula-derivation) | ||
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| (Sign Convention adapted from | ||
| https://www.toppr.com/ask/content/concept/sign-convention-for-mirrors-210189/) | ||
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| """ | ||
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| 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. | ||
| """ | ||
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| 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 | ||
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| 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 | ||
|
There was a problem hiding this comment.
There was a problem hiding this comment. When running the doctests locally, there were issues when used without the isclose, should i still remove them or leave it as it is ?
There was a problem hiding this comment. Is there anything else I should add/change ?, or just have to wait till PR is merged ? |
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| >>> object_distance(90, 0) | ||
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There was a problem hiding this comment.
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| Traceback (most recent call last): | ||
| ... | ||
| ValueError: Invalid inputs. Enter non zero values with respect | ||
| to the sign convention. | ||
| """ | ||
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| 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 | ||
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| 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) | ||
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There was a problem hiding this comment.
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| Traceback (most recent call last): | ||
| ... | ||
| ValueError: Invalid inputs. Enter non zero values with respect | ||
| to the sign convention. | ||
| """ | ||
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| 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 | ||
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