"Because it alters the direction of the rays in a definite way as is described in textbooks on physics," is the reply one hears most often. This, however, is but a remote reason, one having no relation to the real cause. So what really causes the microscope and telescope to magnify?
To help understand why the angle of vision is so essential, let's refer to a significant feature of our eye. Every object or part of an object that we observe at an angle of less than one minute appears to the normal eye as a point with no distinguishable shape or elements.
When an object is far away or so small that the whole of it, or parts of it, are observed at an angle of vision less than one minute, we cease to make out its details. This is because at this angle of vision the retinal image of the object or its element covers only one visual cell, with the result that we see a point and nothing more.
When people say that a microscope has a magnifying power of 100, they mean that it presents objects at an angle of vision 100 times greater than the angle at which we would see them without the instrument. If an optical instrument does not increase the angle of vision, it will not magnify at all, even if we think we are seeing a magnified object.
When low on the horizon, the moon seems much larger than when high up in the sky; but we fail to detect on this enlarged disc anything new, which we didn't notice when our nocturnal luminary was high in the sky.
Taking the case of magnification Edgar Allen Poe (The Sphinx) describes, we shall again see that no new details were observed in the magnified object. The angle of vision remains constant, but the butterfly is observed at one and the same angle whether removed further away or brought up close to the window.
Since the angle of vision does not change, the enlarged object, however staggering, doesn't reveal a single new detail.
But to the reader familiar to The Sphinx by Edgar Allan Poe, one can explain why the microscope gives the details, which Edgar Allan Poe's observer failed to see in his monster butterfly. The microscope gives not just an enlarged image and nothing more; it presents the object at a greater angle of vision.
Hence the retinal image is larger, covering a bigger number of visual cells and thus supplying a bigger number of visual cells and thus supplying a bigger number of visual impressions. In short, the microscope magnifies not the object but its retinal image.