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I read this short story some years ago, and I’m unable to find it since. The story was about some scientists who engineer a sort of telescope that can see to the end of the Universe. They initially see a large dot, and eventually realise that it’s moving from side to side very slowly. They somehow find out that the dot is the pupil of a giant eye, and it’s revealed that their world exists within a larger universe, and they are being viewed by the inhabitants of that universe through a microscope.

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    Hi, welcome to SF&F. When was "some years ago?" Do you recall where you read this? Check out the suggestions for story-identification questions to see if they help you recall any additional details you can edit into your question.
    – DavidW
    Dec 8, 2020 at 20:54
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    Sounds Philip K. Dickensian. Dec 8, 2020 at 21:41
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    It sounds more "before the golden age" to me ... Dec 9, 2020 at 6:49

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Possibly Colossus by Donald Wandrei published in 1934. It is similar to your story though different in some details.

The astronomer Professor Dowell invents a super-telescope, but he finds that at a certain distance the universe seems to end and he can see nothing beyond it:

The astronomer motioned toward the calculations. “You remember when you were here the day before yesterday? And I showed you photographs we made of the thirty-first magnitude nebulae in the Orion group?”

“Of course! You said they marked a milepost in astronomy.”

“Did I? Yes, yes; to be sure. Just to think that only eighteen magnitudes were visible until we built this telescope, and now there are thirty-one, while the known universe has been expanded to nearly a billion light-years.”

“Don’t!” protested Duane. “That’s too much!”

The professor did not hear him. ‘I’m puzzled about a phenomenon of the thirty-second magnitude.”

“What is it?”

“There is no thirty-second magnitude!

He eventually works out that this is because our universe is embedded in bigger universe, and what he has seen is the edge of our universe. The protagonists build a space ship, the White Bird, to travel to edge of the universe and see what is beyond it.

Duane and the love interest Anne travel to the edge of the universe (Anne dies on the journey) and at the edge Duane bursts through to the larger universe. This is where the pupil is mentioned because Duane finds himself on a microscope slide:

When Duane’s dazed faculties began to function again, it was with a feeling of the deepest awe that he stared around and tried to comprehend what had happened. Realization came slowly, and he found it difficult even to decipher his surroundings.

Light flooded his compartment, bright white light that was curiously restful and soothing to his eyes, unlike the glare of the Sun. The White Bird rested on a flat plain of what looked like glass, perhaps a hundred yards long and ten wide. Far below him he saw a second plain, mahogany-colored, which swept away in the distance, then stopped at a sheer cliff that fell an unknown distance down toward the blur of what seemed to be solid ground. From the second level rose two brasslike towers that supported the glassy oblong upon which the White Bird rested.

What did this mean? He looked upward. What was that giant circle overhead?

He peered out. What were those colossal and serrated monuments that looked like the mechanism of giants and possessed eerie illusions of a four-dimensional geometry? What were those other massive bulks that towered toward the spaces above? Understanding, and fright paralyzed him in a flash of intuition.

The White Bird reposed on the slide of a microscope! The second plain was a table top, the third plain a floor. The geometric metallic mountains were apparatus and machines. The towering things were living beings. He had burst through the atom that was his universe and had emerged on a planet of a greater universe, a superuniverse!

Though I think the giant circle is the microscope lens not a pupil, and there is no mention of it moving from side to side.

There are many stories from the pre-war period in which there were universes within universes, for example The Universe Ranger by Stanton A. Coblentz also describes a super telescope that can see to the edge of our universe and out into the super universe surrounding it. However there is no eye observing our universe in this story.

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Some elements match The Ifth of Oofth, by Walter Tevis. You can read it here.

Spoilers ahead.

A scientist invents a multi-dimensional space inside a small box. He looks into it and sees a small misty ball. Then an eye appears in the sky. He works out that the internal space in the box has wrapped itself around Earth, and the eye is his own.

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