Reflection and refraction of light

[skierface]

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!

 

[rude man]

Draw a picture. Use Snell's law to construct a triangle formed of the incident and refracted rays and your spear's path.

 

[skierface]

Just tried that. Not successful. I got an angle of 31 degrees, but that's not right. :(

 

[rude man]

Show your work. Preferably show your diagram, otherwise describe it verbally.

 

[Nickie]

I can provide a response to this problem by using the principles of reflection and refraction of light. Firstly, when light travels from one medium to another, such as from air to water, it undergoes refraction, which is the bending of light. This is due to the change in speed of light as it moves from one medium to another. In this case, the light from the target at the bottom of the pool will bend as it reaches your eyes, making the target appear higher than it actually is.

To calculate the angle at which you should throw the spear, we can use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speeds of light in the two media. In this case, the angle of incidence is 30 degrees, the angle of refraction is 90 degrees (since the light will be traveling along the surface of the water), and the speed of light in air is approximately 3x10^8 m/s while in water it is approximately 2.25x10^8 m/s.

Using this information, we can set up the following equation:

sin(30 degrees) / sin(90 degrees) = (3x10^8 m/s) / (2.25x10^8 m/s)

Solving for the unknown angle of refraction, we get:

sin^-1 (sin(30 degrees) x (2.25x10^8 m/s) / (3x10^8 m/s)) = 22.62 degrees

This means that in order to hit the target, you should throw the spear at an angle of 22.62 degrees below horizontal, taking into account the refraction of light. However, this calculation assumes that the spear travels in a straight line, which may not be completely accurate in reality. The actual angle may vary slightly depending on the speed and trajectory of the spear.