Apparent depth of coin in water using Snell's law

[benhorris]

A student decides to use the tank and water to make a side-show game to raise money at a fete. She places a coin on the bottom of the tank and invites people to drop more coins into cover it – apparently easy to do until you try it. The water is 0.5 m deep. When someone looks vertically into the tank, how far below the surface does the coin appear to be?

Please help, i have no idea how to do this...

thank you... :-)

 

[Doc Al]

Consider the coin as a source of light. Follow a ray of light (at some angle $\theta$ to the normal) from the coin through the water and into the air. Which way does it bend when it hits the air? By what angle? So, considering the light from the coin after it gets bent at the surface and hits your eye, where does the coin appear to be? (Extend the ray of light that hits your eye straight back to find the apparent position of the source.)

 

[wais]

To calculate the apparent depth of the coin, we will need to use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media involved. In this case, the two media are air and water.

First, we need to determine the angle of incidence. This can be done by drawing a diagram, where the normal line (perpendicular to the surface of the water) intersects with the incident ray (the line from the observer's eye to the coin). The angle between these two lines is the angle of incidence.

Next, we need to determine the angle of refraction. This can be done by using Snell's Law and the indices of refraction for air and water. The index of refraction for air is 1, while the index of refraction for water is 1.33.

Once we have both angles, we can use the formula for Snell's Law to calculate the apparent depth of the coin. This can be done by rearranging the formula to solve for the distance below the surface, which would be the apparent depth.

It may be helpful to look up a tutorial or example problem on Snell's Law to get a better understanding of the process. Good luck with your side-show game and fundraising efforts!