Height Ratio of A Coin below the Water

In summary, the conversation discusses a scenario where a coin appears to be in a shallower depth in a pool compared to its actual depth. The conversation also mentions the use of Snell's law of refraction and trigonometry to solve the problem.
  • #1
willydavidjr
66
0
A coin is at the bottom of a pool with a depth of [tex]h^l[/tex][m]. The diagram I provided below shows the coin can appear to be in a place shallower than its actual depth.

Looking perpendicularly onto the water surface ( [tex]i\cong 0, r\cong 0[/tex] ), the coin looked as if it were in a place with depth h[m]. FInd the ratio of [tex]h^l[/tex]/h of the two heights.

This is the site of the diagram: www.geocities.com/willydavidjr/coin ...
 

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  • #2
Well, where's your solution? Apply Snell's law of refraction--and a bit of trig--and you can solve it. Hint: Consider small angles of incidence and refraction (close to the normal).
 

1. What is the height ratio of a coin below the water?

The height ratio of a coin below the water refers to the distance between the surface of the water and the top of the coin when it is fully submerged. This ratio can vary depending on factors such as the size and density of the coin, as well as the depth and temperature of the water.

2. Why does the height ratio of a coin below the water change?

The height ratio of a coin below the water changes because of the principles of buoyancy. When an object is placed in water, it displaces a certain amount of water equal to its own volume. This creates an upward force on the object, known as buoyancy, which causes the object to appear to weigh less. As more of the coin is submerged, the amount of water displaced increases, resulting in a change in the height ratio.

3. Can the height ratio of a coin below the water be used to determine the coin's density?

No, the height ratio of a coin below the water cannot be used to determine its density. This is because the buoyant force is dependent on the volume of water displaced, not the density of the object. To accurately determine the density of a coin, other methods such as measuring its mass and volume would need to be used.

4. Is the height ratio of a coin below the water the same in all types of water?

No, the height ratio of a coin below the water can vary depending on the type of water it is placed in. This is because the density of water can vary depending on factors such as salinity and temperature. For example, a coin will appear to be more submerged in saltwater compared to freshwater, even if the height ratio remains the same.

5. How can the height ratio of a coin below the water be affected by external factors?

The height ratio of a coin below the water can be affected by external factors such as air pressure, temperature, and the presence of other objects or substances in the water. These factors can affect the buoyant force acting on the coin and result in a change in the height ratio. Additionally, surface tension and water currents can also impact the height ratio of a coin below the water.

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