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In a simple convex lens when object is placed at principal focus, we can not see the image because it is at infinity. Then how can we see the final image formed by an astronomical telescope which also lies at infinity?

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You cannot see an image formed at infinity unless you go there to look at it. An infinite conjugate image is the same thing as collimated light, or afocal. The rays from a particular field point are parallel to each other rather than converging or diverging as they would for a real or virtual image respectively. The only way you can SEE an image in collimated light is to use a lens to FORM that image. Your eye is a good example of this. A typical telescope consiste of an objective lens and an eyepiece lens. The Objective lens has a long focal length and forms a real image in the front focal plane of the eyepiece. Since that image is in the front focal plane of the eyepiece, the light is collimated coming out of the eyepiece (image at infinity). But when you place your eye behind the eyepiece, the lens in your eye forms a real image onto your retina. Hence, you can now see that image because your eye lens has converted it to a real, and finite, image.

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You can see the image "at infinity". All you need to do is set up your eyes to focus on a distant object. You can do this by closing your right eye and looking at a distant object with your left eye. Now open your right eye and use it to look through the lens.

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  • $\begingroup$ How big would an object an infinite distance away have to be to see it ? $\endgroup$ – Martin Beckett Aug 26 '16 at 4:31
  • $\begingroup$ Here I used the word infinity as a synonym for distant object. In theory the light from an object an infinite distance away will be parallel and the image would be formed in the focal plane of a lens. In practice a distant object (many times the focal length of the lens) produces light which is approximately parallel and so produces an image which is to a good approximation in the focal plane of the lens. $\endgroup$ – Farcher Aug 26 '16 at 4:54
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First, in your example, the two situations described are different. For astronomical objects, the object is at infinity and the image is formed in the focal plane of a convex lens (and not at infinite). You can see this by projecting the image of the sun on a piece of paper.

However, if you ask about the situation when indeed the image would be formed at infinity, remember that besides the lens forming the image there is another one in your eye. This second lens can (if the eye if properly adapted, as described by previous post) project the image on the retina rather than very far away.

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