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Snell's Law and Prisms watch

1. 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.
2. (Original post by zackdove)
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.
3. (Original post by Joinedup)
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.
Worrying about significant figures comes later in the write up so that's fine.

I've already got 10 sets of measurements using my triangular prism so I'm stuck with it now! All I really need to know is how to derive that awful formula.
5. That looked promising but that's just for the angle of minimum deviation where the beam is parallel to the 'base' of the prism.
6. (Original post by zackdove)
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?
7. (Original post by Joinedup)
I think the one in the OP is too, where did you find it?
Yeah the one in OP is as well... ****.
I'm trying to draw it all out and do it with trig but I'm stuck.
8. sin i
____

sin r

I think that's Snells Law, where 'i' is the incidence of the light ray and 'r' is the refraction.
9. (Original post by aamirac)
sin i
____

sin r

I think that's Snells Law, where 'i' is the incidence of the light ray and 'r' is the refraction.
Yeah that's the easy part! I'm trying to fit Snell's Law into a prism where I can work out the refractive index from the angle of deviation which I've measured.
10. (Original post by zackdove)
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 where is the angle of deviation, and is the angle of the prism.
11. (Original post by atsruser)
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 where is the angle of deviation, and 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.
12. (Original post by zackdove)
The angle was ~60 so i think I'm ****ed...
You are, from the POV of the small angle stuff, yes, and you can't use minimum deviation, as you haven't measured that.

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 don't have time to think about the general case at the moment, but I'll have a go on Tuesday and see if I can come up with something useful. A quick Google turns up nothing, which suggests that it gets messy, but I can't quite see why it should be so difficult - geometrical optics is full of approximations though, and this might be one case where you need them.
13. 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/simg23...dispersion.pdf
14. (Original post by Joinedup)
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/simg23...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/scienc...tml#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
15. (Original post by zackdove)
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/scienc...tml#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.
16. (Original post by Joinedup)
suit yourself, but remember that you might lose marks if you don't round off to an appropriate number of sf.
Will do!
17. (Original post by zackdove)
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 , 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.
18. (Original post by atsruser)
I've had a go at this. I have ended up with something for which it is impossible to solve for , 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!
19. (Original post by zackdove)
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!
I've attached my derivation, relating being total deviation, initial angle of incidence, final angle of refraction and refractive index resp. I can't vouch for correctness.

It may give you something which you can use to solve by trial-and-improvement for .
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