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