# Aquarium/refractive indices/detector

Quick question: I'm currently fiddling around with this homework of mine and I seem to be lacking some basic optics knowledge apparently.

An aquarium is filled with a fluid as seen in the figure below. 10cm above the water surface under an angle $\alpha=58°$ to the normal a light beam is irradiated. Directly under the aquarium a detector can be moved. The thickness of the aquarium is about 0.5cm and the refractive index of glas is n=1.52.

With an unknown fluid the detector has to be moved away by 243.00 mm from its original location so that the outgoing light beam can hit the detector. What's the refractive index of that fluid?

Alright, I tried drawing the situation and denoting some things (don't pay any respect to my artistic ability):

Now, I couldn't find an approach to solve this problem. I tried applying Snell's Law in any way possible and got nowhere. My question is: Does the $\gamma$ that I have denoted in my picture have the same magnitude as $\alpha$? Because if that's the case I can easily calculate $\beta$ using Pythagoras. Otherwise I seriously don't know how to go about this problem.

• Yes it is, but you should write the $\frac{n_1*sin(\theta_1)}{n_2*sin(\theta_2)}$ equations for each interface and verify it for yourself. – Carl Witthoft Nov 8 '15 at 16:45
• The initial angle alpha, Snell's law and a little trigonometry should be all you need to solve the problem. – Samuel Weir Nov 8 '15 at 20:10
• @CarlWitthoft You're both right. Brain-fart on my part. – Rab Nov 8 '15 at 20:55