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.
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.
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.
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.
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.
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.
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.
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'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!
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 D,θi,ϕr,n 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 n.