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When two lenses are in combination, what logic is it to take the image of the first lens (which is not formed in real) as a virtual object to the second lens?

enter image description here

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    $\begingroup$ What does "real" mean ? (rhetoric question) The light rays exist before and after what you're calling the "image". The "logic" is just a mean of calculus/drawing. $\endgroup$
    – TZDZ
    Commented Nov 24, 2014 at 15:56

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You're mixing reality with the process of image formation.

The object v is an auxiliary object when we perform calculations via stage 1 and stage 2. But actually, what really happens is that the rays bend a little bit after lens 1 and then they tilt again in the second lens. The result is the image $v1$ formed there.

The thing is that we calculate it in two steps, and we say that, for all practical purposes, it is like if we only had lens 2, and LIKE IF the object were v, but this is only an auxiliary reasoning.

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Implicitly, this is what happens when we look at an image through a magnifying glass (a convergent lens).

When one looks directly at an image which is in a plane $P$ at a distance $x$ from one’s eye, an image of the object is formed on the retina. If the object is not too close, the lens in the eye is strong enough to form a clear (focused) image on the retina and we see the object clearly.

When one looks at the same image through a magnifying glass, one looks at a bundle of rays (a bundle of parallel rays is the image it located precisely at the focus of the lens). In this case, it is easier for the eyes to form a clear image on the retina, because the eye’s lens is not dealing with divergent rays coming from the points of a real (close) object, but with a bundle of parallel rays seemingly stemming from a virtual image of the objet located at an infinitely remote location further away from the eye.

enter image description here

In other words, the intermediate image, real (as in Newton’s telescope) or imaginary (as in Galileo’s binoculars) is just a mathematical device, an artefact, an intermediate construct, an abstraction aimed at solving a problem by a method of « divide to conquer »: splitting a complex problem into smaller, simpler problems which can be tackled separately and merged in a later stage to provide the final answer to the problem.

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