Using a transparent cup of water as a magnifier When a transparent glass of water is placed in front of a striped background, it appears to produce this “magnified” view of the background in the center of the cup (i.e., the v shaped blue thing in the middle)

Just going from visual cues, this magnification seems to be dependent on the diameter of the glass, with lower diameter (bottom of the glass) having lesser magnification compared to the top. I am struggling to get an intuitive picture of what's causing this magnification. Would appreciate any thoughts on this.

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*It also seems like an interesting (but inefficient) way to magnify the background. Scaling this cup by a few hundred or a thousand times, might actually make a decent microscope. :)

 A: The cup (rather the water in it) simply acts like a thick cylindrical lens. When looking through it at an object close to the cup, it acts much like a magnifying glass, but one that magnifies only in one direction (perpendicular to the cylinder axis).
While you would put a magnifying glass about a focal length $f$ away from the object, you would put the cup about one radius ($R$) away for the best magnification. Then, in terms of magnification, the cup acts like a magnifying glass with a focal length of ~$2R$.
The apparent angular magnification you are seeing in that photo is not how you would normally define magnification. For a magnifying glass, the magnification would typically be defined relative to the closest distance at which you can comfortably view the object, usually taken to be $25 \text{ cm}$. When you are looking through the cup from a comfortable distance away, the magnification would be $(25\text{ cm})/2R$ (the corresponding magnification for a magnifying glass is $(25\text{ cm})/f$). This shows that you can actually achieve better magnification by looking through the cup close to the bottom where the radius of curvature is smaller.
The reason your photo appears to contradict this is that to achieve the best magnification, you would adjust the distance of the cup from the object as you look through it. The optimum distance is proportional to $R$. For small $R$ near the bottom of the cup, the cup is too far away from the object to achieve maximum magnification, so the magnification is low.
