Snell's Law and Prisms

For my A2 Physics Coursework (OCR B), I'm doing an investigation on the refraction of light through sugar solution, where I shine a laser through different sugar solutions in a triangular prism and measure how far up the beam is shifted. I'm going to work out the refractive index of each concentration but working out the refractive index is horrible when working with prisms apparently.

After searching online I've managed to pull the equation n=2.00056×sin(0.5(θ+60°)) out of somewhere but I kind of need to prove that I can derive the equation, trusting that it's actually even right...
If there are any trigonometry gods out there I'd really appreciate some help.

have a think about how many significant figures you're likely to be working to...

tbh I'd suggest ditching the triangular prism and using either a hemicylinder or a rectangular dish - it'll make measuring angles easier as well as simplifying the maths.

how about this... http://www.a-levelphysicstutor.com/optics-prisms.php

That looked promising but that's just for the angle of minimum deviation where the beam is parallel to the 'base' of the prism.

I think the one in the OP is too, where did you find it?

sin i
____

sin r

I think that's Snells Law, where 'i' is the incidence of the light ray and 'r' is the refraction.

For my A2 Physics Coursework (OCR B), I'm doing an investigation on the refraction of light through sugar solution, where I shine a laser through different sugar solutions in a triangular prism and measure how far up the beam is shifted. I'm going to work out the refractive index of each concentration but working out the refractive index is horrible when working with prisms apparently.

After searching online I've managed to pull the equation n=2.00056×sin(0.5(θ+60°)) out of somewhere but I kind of need to prove that I can derive the equation, trusting that it's actually even right...
If there are any trigonometry gods out there I'd really appreciate some help.

I suspect that this is going to be tricky in general unless you are working with the angle of minimum deviation, or if you have a small-angle prism (of about 5-6 degrees, say) as then you get the approximate relationship $d=(n-1)A$ where $d$ is the angle of deviation, and $A$ is the angle of the prism.

The angle was ~60 so i think I'm ****ed...

My physics teacher is useless so I think I might ask my Maths teacher to work some trig magic and pray that it somehow works out.

maybe the eqn in the bottom half of p.3 if you were running your experiment with a constant angle of incidence to the first face of the prism.

https://www.cis.rit.edu/class/simg232/lab2-dispersion.pdf

This equation looks the most correct so cheers!

Strangely though, out of all the possible equations I've found;
http://www.a-levelphysicstutor.com/optics-prisms.php
and
http://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p028.shtml#background
Give me the most accurate answers when I use the value for water... I think I'll stick with the a-levelphysicstutor one and even though its wrong I'll just hope they dont notice

suit yourself, but remember that you might lose marks if you don't round off to an appropriate number of sf.

The angle was ~60 so i think I'm ****ed...
My physics teacher is useless so I think I might ask my Maths teacher to work some trig magic and pray that it somehow works out.

I've had a go at this. I have ended up with something for which it is impossible to solve for $n$, refractive index, without either making approximations (which I don't think will hold with your measurements), or by using numerical methods (like Newton-Raphson, or whatever). I can put up the results that I've got so far if you want, but I'm afraid that they probably won't help you.

I'm pretty sure it is impossible to solve. I don't think that they will help but I'd love to see your work anyway!