Object magnified inside a cylinder of water

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Would you able to tell me what’s the ideal angle Of a curved glass in order to Magnify an object inside an aquarium to the maximum. Also what would be the ideal distance of the object inside the aquarium. Sorry if I didn’t explain myself properly. I‘m hopeful somebody would be able to explain it to me. Let’s make the world a better place.
✌🏼 peace and love

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First, your diagram seems to show the fish looking smaller. You could call that magnification by a fraction, but that doesn't sound like what you meant.

To make it look bigger, the glass (acrylic) needs to curve the other way - convex on the air side.
Both the curvature and the distance of the fish will affect the magnification.

Quick calculation, I'd say max magnification when the fish is 4x further away than the radius of the glass. That puts it at the focus of the lens made by the curved water surface. If the fish is nearer the side, it will be less enlarged. If further away it will be out of focus until it is far enough away to make an image between the observer and the tank. If you stand well back, this could be even more enlarged, but upside down.

My guess is you'd be best served by having the focus around the farthest point you'd want to look at the fish. If that's the far side of the tank, then the radius of the side would be at least a quarter of the width (sideways depth?) of the tank. But the greater the curvature, the more distortion you get and I'd guess you wouldn't want more than 20 degrees of arc over the side.

Having a cylindrical side will only magnify in one direction, distorting the shape of the fish.

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As an artist you may also be familiar with the difference in index of refraction at the boundary between air and water; both called fluids in physics. A straight stick placed into a cylinder of water appears to bend; an effect Salvador Dali and David Hockney loved to exploit in paintings.
Hockney Pool with Two Figures

Some species of fish have two pair of eyes, one for looking up through air, the lower pair attuned to water vision.
Anableps at surface.

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Cutter Ketch
I don’t know if you will enjoy your stretched fish. The cylinder will only magnify in one dimension. If you would like less distorted fish, use a spherical surface like the classic fish bowl aquarium.

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My guess is you'd be best served by having the focus around the farthest point you'd want to look at the fish.
Although it might be visually interesting to have the fish swimming through the focus (point or line, depending upon geometry) and getting huge. Incidentally using the index of water as 1.33 I get the focus at 3R not 4R for a single surface lens...the plexiglass is thin Ii presume...

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Nik_2213
Plan _B could be to stick a 'Fresnel-type' magnifier panel on the front...

Given cautious heating, a sufficiently large radius and due care, a flexible acrylic A4/Legal sheet might be shaped to fit a cylindrical aquarium...
;-)

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Summary:: As an artist I find it challenging to understand some of the concepts of physics - I admit I’m not good at it but I’m willing to learn to make the world a better place for us and the next generations 💪🏼

Also what would be the ideal distance of the object inside the aquarium.
As an artist, you would be used to observing and experimentation so I suggest you study the effect with a range of glasses and jars with different radii. Move a pencil around inside it (back and forth and side to side) and see what happens to the image you see. I try to do experiments whenever possible and they often only involve the stuff you can find in the kitchen.

The 'strength' of a lens depends on the radius of curvature of the surface, although most simple lenses are operated with air on both sides. Look at the various eyeglasses of your friends and you will see the stronger ones are thicker / more curved. (Not the whole story because more expensive materials are sometimes used so my simple rule won't always apply.)

In the case of your aquarium problem, you will probably find that a large glass cylinder will produce less distortion / 'magnification' than a small one and, of course, what you see will also include stuff that's outside the water, on the other side.

Peace and love back to you.

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First, your diagram seems to show the fish looking smaller. You could call that magnification by a fraction, but that doesn't sound like what you meant.

To make it look bigger, the glass (acrylic) needs to curve the other way - convex on the air side.
Both the curvature and the distance of the fish will affect the magnification.

Quick calculation, I'd say max magnification when the fish is 4x further away than the radius of the glass. That puts it at the focus of the lens made by the curved water surface. If the fish is nearer the side, it will be less enlarged. If further away it will be out of focus until it is far enough away to make an image between the observer and the tank. If you stand well back, this could be even more enlarged, but upside down.

My guess is you'd be best served by having the focus around the farthest point you'd want to look at the fish. If that's the far side of the tank, then the radius of the side would be at least a quarter of the width (sideways depth?) of the tank. But the greater the curvature, the more distortion you get and I'd guess you wouldn't want more than 20 degrees of arc over the side.
View attachment 257862

Having a cylindrical side will only magnify in one direction, distorting the shape of the fish.
First, your diagram seems to show the fish looking smaller. You could call that magnification by a fraction, but that doesn't sound like what you meant.

To make it look bigger, the glass (acrylic) needs to curve the other way - convex on the air side.
Both the curvature and the distance of the fish will affect the magnification.

Quick calculation, I'd say max magnification when the fish is 4x further away than the radius of the glass. That puts it at the focus of the lens made by the curved water surface. If the fish is nearer the side, it will be less enlarged. If further away it will be out of focus until it is far enough away to make an image between the observer and the tank. If you stand well back, this could be even more enlarged, but upside down.

My guess is you'd be best served by having the focus around the farthest point you'd want to look at the fish. If that's the far side of the tank, then the radius of the side would be at least a quarter of the width (sideways depth?) of the tank. But the greater the curvature, the more distortion you get and I'd guess you wouldn't want more than 20 degrees of arc over the side.
View attachment 257862

Having a cylindrical side will only magnify in one direction, distorting the shape of the fish.
Hello thank you so much for all the information you shared with me. It was very helpful! 🙂 So basically what I need now is to calculate the radius of the curvature so I’ll be able to A
Plan _B could be to stick a 'Fresnel-type' magnifier panel on the front...

Given cautious heating, a sufficiently large radius and due care, a flexible acrylic A4/Legal sheet might be shaped to fit a cylindrical aquarium...
;-)
First, your diagram seems to show the fish looking smaller. You could call that magnification by a fraction, but that doesn't sound like what you meant.

To make it look bigger, the glass (acrylic) needs to curve the other way - convex on the air side.
Both the curvature and the distance of the fish will affect the magnification.

Quick calculation, I'd say max magnification when the fish is 4x further away than the radius of the glass. That puts it at the focus of the lens made by the curved water surface. If the fish is nearer the side, it will be less enlarged. If further away it will be out of focus until it is far enough away to make an image between the observer and the tank. If you stand well back, this could be even more enlarged, but upside down.

My guess is you'd be best served by having the focus around the farthest point you'd want to look at the fish. If that's the far side of the tank, then the radius of the side would be at least a quarter of the width (sideways depth?) of the tank. But the greater the curvature, the more distortion you get and I'd guess you wouldn't want more than 20 degrees of arc over the side.
View attachment 257862

Having a cylindrical side will only magnify in one direction, distorting the shape of the fish.
Thank you so much for all the explanation, it was very helpful to begin with.
Summary:: As an artist I find it challenging to understand some of the concepts of physics - I admit I’m not good at it but I’m willing to learn to make the world a better place for us and the next generations 💪🏼

Would you able to tell me what’s the ideal angle Of a curved glass in order to Magnify an object inside an aquarium to the maximum. Also what would be the ideal distance of the object inside the aquarium. Sorry if I didn’t explain myself properly. I‘m hopeful somebody would be able to explain it to me. Let’s make the world a better place.
✌🏼 peace and love
Thank you so much for your valuable advice. It was definitely a good start but still I have some challenges such as how to calculate the curvature of the glass in order to calculate the right distance of the object inside the tank (I looked the formula online but it seems very complicated to me). Also I made this sketch of what I have in mind so hopefully it is easier for you to have an idea of what I want to achieve. The dimensions of the tank, the curvature of the glass and the size of the object inside can be changed in order to get the desired magnification. Based on that image what are your thoughts? Thank you so much again! :)

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Plan _B could be to stick a 'Fresnel-type' magnifier panel on the front...

Given cautious heating, a sufficiently large radius and due care, a flexible acrylic A4/Legal sheet might be shaped to fit a cylindrical aquarium...
;-)
What exactly is a 'Fresnel-type' magnifier panel? I would need something as large as 80 cm long. Thank you!

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I don’t know if you will enjoy your stretched fish. The cylinder will only magnify in one dimension. If you would like less distorted fish, use a spherical surface like the classic fish bowl aquarium.
Do you think something like that or similar would work? thank you!

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Make it glow art
As an artist, you would be used to observing and experimentation so I suggest you study the effect with a range of glasses and jars with different radii. Move a pencil around inside it (back and forth and side to side) and see what happens to the image you see. I try to do experiments whenever possible and they often only involve the stuff you can find in the kitchen.

The 'strength' of a lens depends on the radius of curvature of the surface, although most simple lenses are operated with air on both sides. Look at the various eyeglasses of your friends and you will see the stronger ones are thicker / more curved. (Not the whole story because more expensive materials are sometimes used so my simple rule won't always apply.)

In the case of your aquarium problem, you will probably find that a large glass cylinder will produce less distortion / 'magnification' than a small one and, of course, what you see will also include stuff that's outside the water, on the other side.

Peace and love back to you.
Hello thank you for your suggestion! I will go to the kitchen and look for some glasses and see what happens. Since the larger the cylinder or curvature of the glass the less magnification I would get, do you think that a tank like that could work?

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I don’t know if you will enjoy your stretched fish. The cylinder will only magnify in one dimension. If you would like less distorted fish, use a spherical surface like the classic fish bowl aquarium.
what about a tank like that?

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Although it might be visually interesting to have the fish swimming through the focus (point or line, depending upon geometry) and getting huge. Incidentally using the index of water as 1.33 I get the focus at 3R not 4R for a single surface lens...the plexiglass is thin Ii presume...
The plexiglass could be as thick as 1 inch or 2.54 cm. The thicker the plexiglass the more magnification can be achieved? Thank you :)

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What exactly is a 'Fresnel-type' magnifier panel? I would need something as large as 80 cm long.
That type of flat lens is used in old OHPs. They are around A4 size and have a focal length of around 1m (1Diopter). Google throws up all sorts of adverts and it will cost you £10 +. Whether it's worth it as an experiment is up to you. O would imagine I would have bought one if I had fish. The cost a acrylic sheet would be strong enough for a home made lens would be more.

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The plexiglass could be as thick as 1 inch or 2.54 cm. The thicker the plexiglass the more magnification can be achieved? Thank you :)
I was thinking that the plexi would be of uniform thickness but curved into shape (either cylinder or spherical) so the water actually "makes" the lens. The plexi thickness then is not optically important.
I think @sophiecentaur idea of a fresnel lens is great particularly for playing with the concept. They are really inexpensive. Seems to me they used to be made (decades ago obviously) to magnify TV set screens and were bigger than A4 size. I'll look a little bit and report any success..

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Just google "giant fresnel lens"

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Although it might be visually interesting to have the fish swimming through the focus (point or line, depending upon geometry) and getting huge. Incidentally using the index of water as 1.33 I get the focus at 3R not 4R for a single surface lens...the plexiglass is thin Ii presume...
Yes, better to stay inside the focus point.

I also neglect the wall thickness and use index of water 4/3 near enough 1.33, but still find focus as shown in the diagram (by my own geometry.)
https://www.math.ubc.ca/~cass/courses/m309-01a/chu/MirrorsLenses/refraction-curved.htm using the same geometry, gives a formula
$$f=\frac{Rn_2}{n_2-n_1}$$
which seems to give ##f=\frac{1.33}{1.33-1}R = 4.03R## (or 4R using 4/3 instead of 1.33)
This site uses a different analysis to get $$\frac{μ_2}{v}-\frac{μ_1}{u} = \frac{μ_2-μ_1}{R}$$
which for ##u=∞ \text{ and } v=f## gives ##\frac{1.33}{f}=\frac{0.33}{R} \text{ and }f=\frac{1.33}{0.33}R=4.03R##

Of course, like most optics, it's all a bit of a fudge and nothing quite goes exactly where the formulae say. (It amazes me that things look so good through lenses.) And to allow for the mounting errors as you go off axis, I was going to suggest that ##\frac 7 2 R ## is a better bet than ## \frac 8 2 R ## with the added advantage that you'll stay inside the focal length nearer the axis.

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Your tank is fine. Focus is way behind back of tank. Not so much magnification, but little distortion. The fish will be slightly stretched lengthways.

You could deepen (L-R) the tank to get the possibility of a bit more magnification, but you don't have to worry about reaching the focus.
Although max magnification sounds nice, maybe some magnification without much distortion is better. Experimenting with a plastic Fresnel lens sheet in front of the tank could show you what more magnification looks like.

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Perhaps I have interchanged "1" and "2"...probably not worth worrying about in this context. Yeah I don't know whether the intent here is to magnify the fish or amplify the "visual interest" factor!

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You could deepen (L-R) the tank to get the possibility of a bit more magnification, but you don't have to worry about reaching the focus.
I would say you DO have to worry about reaching the focus. Beyond the focus, the image will turn upside down and look alarming in the process. Convex lenses have two modes- the close up 'magnifying glass' mode and the distant 'projector' mode'.
Get a feel of the topic by buying a cheap magnifying glass and trying it out.
I keep banging on about experimentation but this sort of thing is always taught in School with practical lessons because the lesson is impressive and hard to forget the results. (I say that from the standpoint of someone who really believes that the Maths is God in Physics, too.)

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But look at his tank. The thickness is less than the radius of curvature. The focus is at 4x R. So any plausible increase in depth is going to be well inside f. I had mentioned your problem in an earlier post.

sophiecentaur