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An interaction between two opposites produces a unique outcome. ..."Jules Henri Poincare(1854-1912, One of France's greatest mathematicians)"

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 Author Topic: Find the image for an object in the water  (Read 6687 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
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 « Embed this message on: January 10, 2011, 08:54:51 pm » posted from:Taipei,T'ai-pei,Taiwan

Do you know what is the image you will find if you look down and watch the object?
When light goes through water or any vacuum other than air it bends. In water an object may seem larger and closer than what the object appears to be at the surface. This is called refraction: the bending of light when passing from one transparent material to another. The formula for refraction is described in Snell's Law. The equation for Snell's Law is n1sinθ1=n2sinθ2.  while θ1 is the angle between the ray and the normal in the first medium. θ2 is the angle between the ray and normal in the second medium. When a light bends through water the frequency stays the same while the wavelength varies causing the change in the direction of the ray, making the object appear closer and larger underwater.

The following simulation let you paly with the above case.
An image of eye represents your eye in the simulation, and there is a blue rectangle in the water.
Let us try to find the image for the yellow dot in the following simulation.

Click the play button, and there are many rays will emit from the yellow dot.
There ray will be refracted when they pass water-air surface.
When the rays are all drawn, it will find the image (red dot) for the yellow dot.

You can drag the yellow to other position (within the blue rectangle) and click play again to find another image point.
The position of the rectangle or the eye can be changed with drag and drop, too!

The range for the emitter rays can be adjusted with those two sliders (ci=0, cf=$\pi$, default value).

You are welcomed to check out related simulation at An object under the water look differ! (Location and shape)

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An interaction between two opposites produces a unique outcome. ..."Jules Henri Poincare(1854-1912, One of France's greatest mathematicians)"

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