Why does water magnifies, and how does it work?

Question

Need to explain to a second grader, How water magnifies naturally when looking through a plastic two liter bottle of water?

Answer 1

It’s not the water alone that magnifies. If you drop a coin in a glass and look down on it, through the open top of the glass, it appears the same size in or out of the water. Look at it through the curved side of the glass and you will see a magnified image. The magnification comes from two things: (1) the index of refraction of the water and its container, compared to the index of refraction of air; and (2) the curvature of the container.

The easiest way to demonstrate magnification is with real images and ray tracing, but the image seen through the plastic bottle is a virtual image, which is the only type of image the eye can focus on. This can also be demonstrated with ray tracing, but getting the second grader to understand the concept might be a bit tricky.

First, you have to model a cross-section of the bottle parallel to its base as a double-convex lens. The bottle with the water inside is actually a double-convex cylindrical lens, but let’s not get bogged down in details.

On a piece of paper draw a horizontal line and somewhere near the middle draw a circle to represent the bottle. The line should equally divide the circle into an upper half and a lower half. Now pick an arbitrary point about two or three inches to the right of the outer edge of the circle and call that point the focal point of the bottle lens. If you have a sunny day or a bright light, you can hold the bottle (with water inside) up to the light and move it toward the paper until you can see an image of the light on the paper. That distance is roughly the focal length of the bottle lens.

To see a magnified object when you look through the bottle lens from the left side, the object must be placed between the bottle and its focal point. Draw a vertical line through the center of the circle about two inches high. This will be our reference line for ray tracing the virtual image. Draw a short vertical arrow-head line to the right of the circle, about half-way between the circle and the focal point. This will be the object that is magnified when you look at it from the other side, through the bottle.

The essence of ray-tracing is to draw two lines whose path you know, starting from the same point on the object, and then find the intersection of those two lines at the same point on either the real or virtual image. Because of the location of the object “inside” the focal length of the bottle lens, the traced rays will form a “virtual image”.

Any ray of light parallel to the axis of the lens (the horizontal line) upon entering the lens will be refracted downward in such a manner that it crosses the focal point of the lens.

Any ray of light that goes through the center of the lens will not be refracted but will continue in a straight line through the lens.

That’s all you need to know to ray-trace simple objects with simple lenses.

To ray-trace the bottle lens magnifier, you will need to draw another focal point on the horizontal line to left side of the lens, the same distance from the center as the right focal point. Now draw a horizontal line from the tip of the arrow-head (the object) to the left, through the right edge of the circle, to the vertical line in the middle of the circle. At this intersection, draw another straight line from there to the left-side focal point. Now draw a second line from the tip of the arrow-head through the center of the circle and continuing on through the lens. The intersection of these two lines is where the image of the arrow head will be.

Note, for the object located between the lens and its focal point, the lines through the lens diverge. That means only a virtual image is formed. Extend the two lines backwards to where they intersect beyond the object to form a virtual image. Note that the virtual image is much taller than the original object. Experiment with ray-tracing various locations of the object with respect to the focal point of the lens to see what happens.

If you place the object beyond the focal point of the lens, it will form a real image on the other side of the bottle. You can’t see this image with your eye, but it can form an image on a piece of paper. The object must be well illuminated and the room fairly dark to see this.

For extra credit, and to demonstrate there is nothing special about water (other than its index of refraction is greater than air), try filling different plastic bottles (all the same size) with other transparent liquids like cooking oil, mineral oil, etc. Does the magnification depend on what you fill the bottle with? It does, but you may not be able to see the difference with the unaided eye.

Answer 2

A Magnifying Glass is like haveing Water that has been made Solid. If you were to have a clear enough large piece of Ice that was clear it would do the same exact thing as a Magnifying Glass. Isn't that weird. It concentrates alot of sun light into a smaller beam/spot/ray of light,.. it's like haveing ALL that sun light touching at one little spot... so it's like being close to the sun.

As for Magnifying with a bottle of water to make things biggin in the water, the reverse is also posible. It depends on how the water is bent or shaped. If you can get different shapes of glass/plastic containers and look from different angles it can effect what you see. Try looking for something cubed,.. maybe with rounded corners. That may act more prismatic even though when people talk about prisims in some fields it may be something with three points... like triangular in shape.

Answer 3

Simply put, light slows down. And because it slows down the laws of physics require that it bends.