Reflection and refraction of light

AI Thread Summary
To solve the problem of hitting an underwater target with a spear, one must consider the principles of reflection and refraction of light. The depth of the water is 0.900 m, and the observer's eyes are 3.20 m above the pool bottom, with a gaze angle of 30 degrees below horizontal. Using Snell's law is essential to determine the correct angle for throwing the spear, as it involves calculating the refraction of light at the water's surface. Participants are encouraged to draw a diagram to visualize the angles and paths involved, as this can aid in understanding the relationship between the incident and refracted rays. Accurate calculations and a clear representation of the problem are crucial for finding the correct angle to successfully hit the target.
skierface
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Homework Statement



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 0.900 m deep. You're standing on a small stool that places your eyes 3.20 m above the bottom of the pool. As you look at the target, your gaze is 30 degrees below horizontal. At what angle below horizontal should you throw the spear in order to hit the target?

Your raised arm brings the spear point to the level of your eyes as you throw it, and over this short distance you can assume that the spear travels in a straight line rather than a parabolic trajectory.

So, I really am not sure what to do with this problem. Any help with formulas and such would be greatly appreciated. Thanks a lot!
 
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Draw a picture. Use Snell's law to construct a triangle formed of the incident and refracted rays and your spear's path.
 
Just tried that. Not successful. I got an angle of 31 degrees, but that's not right. :(
 
Show your work. Preferably show your diagram, otherwise describe it verbally.
 
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