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respectively. Applying the invariant to the object and image points implies the product of these magnifications is given by
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are the corresponding quantities in image space. The Smith–Helmholtz invariant implies that the lateral magnification,
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The Smith–Helmholtz invariant also relates the lateral and angular magnification of the optical system, which are
160:. For a given optical system and specific choice of object height and axial ray, this quantity is invariant under
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Principles of optics : electromagnetic theory of propagation, interference and diffraction of light
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Principles of optics : electromagnetic theory of propagation, interference and diffraction of light
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658:. The Smith–Helmholtz is the optical invariant restricted to conjugate image planes.
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and an axial ray passing through the same axial position as the object with angle
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343:. The paraxial version of the sine condition is satisfied if the ratio
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753:(2nd ed.). Amsterdam: Elsevier/Academic Press. pp. 63–64.
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are the axial ray angle and refractive index in object space and
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propagating through an optical system. Given an object at height
640:{\displaystyle {\frac {y'}{y}}{\frac {u'}{u}}={\frac {n}{n'}}}
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The Smith–Helmholtz invariant has a close connection with the
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is constant if and only if the sine condition is satisfied.
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Jenkins, Francis A.; White, Harvey E. (3 December 2001).
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The Smith–Helmholtz invariant is closely related to the
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805:(6th ed.). Pergamon Press. pp. 164–166.
703:(6th ed.). Pergamon Press. pp. 164–166.
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778:(4th ed.). McGraw-Hill. pp. 173–176.
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329:{\displaystyle H=n_{i}{\bar {y}}_{i}u_{i}}
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184:th conjugate image point with height
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725:"Technical Note: Lens Fundamentals"
247:in medium with index of refraction
220:and refracted axial ray with angle
843:. You can help Knowledge (XXG) by
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799:Born, Max; Wolf, Emil (1980).
697:Born, Max; Wolf, Emil (1980).
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213:{\displaystyle {\bar {y}}_{i}}
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125:{\displaystyle H=n{\bar {y}}u}
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88:, the invariant is defined by
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35:is an invariant quantity for
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749:Kingslake, Rudolf (2010).
61:{\displaystyle {\bar {y}}}
33:Smith–Helmholtz invariant
18:Smith-Helmholtz invariant
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380:{\displaystyle nu/n'u'}
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732:. Retrieved
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684:References
162:refraction
305:¯
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734:16 April
662:See also
654:and the
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274:we have
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668:Etendue
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136:where
29:optics
835:This
841:stub
807:ISBN
780:ISBN
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736:2020
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