Snells Law - Problem understanding question

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Discussion Overview

The discussion revolves around understanding a problem related to Snell's Law in the context of a carnival game involving throwing a spear at an underwater target. Participants are trying to clarify the angles involved in the problem and whether the problem statement is correctly formulated.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the angles mentioned in the problem and questions the validity of the problem statement.
  • Another participant inquires whether the refractive index of the water is provided or if it needs to be determined.
  • A different participant argues that the problem is well-posed, noting that the refractive index of water is known and that Snell's Law can be applied to find the refracted angle based on the given angle of incidence.
  • One participant reiterates their confusion about the angles and requests a visual representation to better understand the problem setup.
  • Another participant explains that the line of sight makes a 30-degree angle with the surface of the water, referencing the alternate angles theorem for parallel lines.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the clarity of the problem statement, with some asserting it is well-posed while others express confusion. Multiple viewpoints on the interpretation of the angles remain unresolved.

Contextual Notes

There are uncertainties regarding the assumptions about the angles and the need for the refractive index, which may affect the calculations involved in applying Snell's Law.

maybnxtseasn
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I have no idea what angle it's talking about and also what angle I am supposed to get in this problem. It seems to me like the problem is written wrong. Could anyone please let me know if it is wrong or right. If it's a valid problem could you also post a simple MSPaint drawing of how this should be drawn with the 30degree angle along with the angle I am supposed to find :) thanks!



One of the contests at the school carnival is to throw a spear at an underwater target lying flat on the bottom of a pool. The water is 1.20m deep. You're standing on a small stool that places your eyes 3.10m above the bottom of the pool. As you look at the target, your gaze is 30degrees below horizontal. At what angle below horizontal should you throw the spear in order to hit the target?
 
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were you given the refractive index of the water in the pool or were you asked to find it.
 
The problem seems well-posed to me.

Water has a known refractive index.

If you know the angle of incidence, you can calculate the angle to which the line of sight is refracted below the water. That's Snell's Law.

We are told that the line of sight above the water is 30 degrees from the horizontal. That means that it is 60 degrees from the vertical.

Given the refracted angle and the known depth of the pool you can calculate the point of intersection of the line of sight with the bottom of the pool.

Then it's just a matter of aiming your spear at that point.
 
maybnxtseasn said:
I have no idea what angle it's talking about and also what angle I am supposed to get in this problem. It seems to me like the problem is written wrong. Could anyone please let me know if it is wrong or right. If it's a valid problem could you also post a simple MSPaint drawing of how this should be drawn with the 30degree angle along with the angle I am supposed to find :) thanks!



One of the contests at the school carnival is to throw a spear at an underwater target lying flat on the bottom of a pool. The water is 1.20m deep. You're standing on a small stool that places your eyes 3.10m above the bottom of the pool. As you look at the target,

your gaze is 30degrees below horizontal
Draw horizontal line from your eyes. Your gaze is 30 degrees below that. By the 'alternate angles theorem' for parallel lines, your line of sight also makes a 30 degree angle with the surface of the water.
. At what angle below horizontal should you throw the spear in order to hit the target?
 

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