Here is a homework question that I'm having a hard time understanding:

Out of pure intellectual curiosity you have donned a snorkeling face mask and allowed yourself to sink to the bottom of the pool, face-up. If where you are lying the pool is 2.50 m deep, what is the diameter of the circle (in meters) in which you see your friends scurrying about at the edge of the pool trying to figure out what you have done to yourself this time? The index of refraction of water is 1.33.

I think the question should be approached using Snell's Law, but I'm struggling to find the angles needed to solve for anything. The following is a picture of my attempt, but again it seems useless without knowing the angles.

We have $n_1 = 1$, $n_2 = 1.33$, so

$$ \begin{array} !\frac{\sin \theta_2}{\sin \theta_1} & = \frac{n_1}{n_2} \\ \sin \theta_2 &= \frac{n_1 \sin \theta_1}{n_2} \end{array} $$

I'm pretty sure I'm missing something...can anyone please help me understand the question?

  • $\begingroup$ Welcome, Vanessa. We have the MathJax engine running on the site to render LaTeX alike markup as mathematical notation, so you don't need to scan or photograph paper note. I've done this one for you and you can fine a few notes in the FAQ. BTW--this is good example of how to ask a basic homework question. $\endgroup$ – dmckee Dec 1 '12 at 4:04
  • $\begingroup$ So, I note that so far you have done some work in angular units but the question says explicitly "in meters", so clearly you are not done yet. $\endgroup$ – dmckee Dec 1 '12 at 4:07
  • $\begingroup$ Thanks for the warm welcome, dmckee! I'll keep keep the mathematical notation in mind the next time I post. Also, about the question does that mean that I don't need any angles to solve this problem? I'm not sure I know any other way of approaching it... is there anything that you can suggest? $\endgroup$ – Vanessa Dec 1 '12 at 4:19
  • $\begingroup$ I think your instinct that this is a refraction problem and that means Snell's law is good. So the next question is what is the relationship between those angles and the "diameter of the circle". It might also be useful to see what other data you've been given and how it might apply (but don't insist on using everything every time--sometimes professors are sneaky). $\endgroup$ – dmckee Dec 1 '12 at 4:26
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    $\begingroup$ I would start by drawing a diagram - in fact in almost all physics programs you start by drawing a diagram - then you can work out which angles you need to know $\endgroup$ – Martin Beckett Dec 1 '12 at 4:56

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