What image would appear on a perfect magnifying glass in perfect vacuum with an object at exactly the distance of the focal point?
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1$\begingroup$ In the context of the various types of aberration, how are you defining "perfect"? $\endgroup$– ChemomechanicsMar 22, 2022 at 20:52
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2 Answers
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You would not get any real picture, just parallel light from every point of you object.
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I like to look at it in terms of paraxial Fourier Optics: The object at the focal point distance $f$ will create an outgoing spherical wave:
$w(t,f)=\frac{w_o}{f}\cdot e^{\frac{ikf}{cos\ \theta }} \cdot e^{-\omega \cdot t}$,
where $w_0$ is the amplitude, $k$ is the wavenumber, $\theta$ is the angle between the object and the axis of rotation of the lens, and $\omega$ is the angular frequency.
To compute the image you would see on the lens, you have to compute the intensity of the spherical wave for every on the lens by squaring its amplitude.
