Why Is an Image at Infinity Called Highly Magnified?

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When an object is positioned at the focal point of a convex lens, the resulting image is formed at infinity and is termed "highly magnified." This terminology arises because the light rays exiting the lens are parallel, indicating significant magnification. However, the image is not referred to as "infinitely magnified" because that term implies an unattainable condition. If the object is placed very close to the focal point, the magnification remains large but finite. Thus, the distinction lies in the exact positioning of the object relative to the lens's focal point.
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When an object is placed at the focal point of a convex lens, the image is formed at infinity, yet it is called a highly magnified image. The fact being that after passing through the convex lens the rays run parallel or rather as a beam.

My question is that if the image is formed at infinity why is it not referred to as an infinitely magnified image. But still if we insist in calling the image as highly magnified, then what should be the magnitude of magnification?
 
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If the object is at the focal point, the magnification is infinite. Not sure why you have been told otherwise.

If the magnification is large, but not infinite, that means the object was near, but not at, the focal point.
 
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