How do I find the refractive index in sugar solutions?

[Jane Smith]

For class I conducted a experiment where I made sugar solutions, poured them into a glass prism container and used a laser pointer to find the refractive index. However, while typing in my results I realized I found the angle of deviation instead of the minimum angle of deviation since I didn't adjust the prism so that the refracted light inside the prism was parallel to the side of the prism.

Does that mean I can not use the formula

to find the refractive index? Do I have to redo my experiment? I am at a time constraint so I would even be open to having another aim for my investigation instead of redoing the experiment. I am very confused and my teacher hasn't been much help.

 

[Wrichik Basu]

That formula cannot be used unless the prism is in minimum deviation position.

There is one more way, though I am not sure how to do the experiment. There is a formula: $n = \frac{\text{Apparent depth}}{\text{Real depth}}$ The idea is to put a coin in a beaker, pour the solution over the coin upto a certain height (the real depth). Now, measure the apparent depth of the coin, and use the above formula.

I am not sure how to measure the apparent depth. I have heard that it can be done using microscopes, but I'm not sure.

 

[ehild]

For class I conducted a experiment where I made sugar solutions, poured them into a glass prism container and used a laser pointer to find the refractive index. However, while typing in my results I realized I found the angle of deviation instead of the minimum angle of deviation since I didn't adjust the prism so that the refracted light inside the prism was parallel to the side of the prism.
View attachment 233369View attachment 233370
Does that mean I can not use the formula

to find the refractive index? Do I have to redo my experiment? I am at a time constraint so I would even be open to having another aim for my investigation instead of redoing the experiment. I am very confused and my teacher hasn't been much help.

Do you know angle B?

 

[Jane Smith]

Do you know angle B?
View attachment 233393

I do know angle B, how does this help me?

 

[gneill]

I do know angle B, how does this help me?

Depending upon what angles you did measure, you should be able to reconstruct the light path through the prism in terms of the unknown index of refraction. The algebra may not be trivial.

Can you provide details about the prism and what data you collected? A diagram would be good.

 

[Jane Smith]

Depending upon what angles you did measure, you should be able to reconstruct the light path through the prism in terms of the unknown index of refraction. The algebra may not be trivial.

Can you provide details about the prism and what data you collected? A diagram would be good.

This is how I set up my experiment. Instead of making sure the laser inside the prism was parallel with the the side of the prism, I just made sure to keep the prism in the same position during the entire experiment. I marked the points b and d as I put the laser through the solutions.

 

[gneill]

Do you have measurements for the distances bc, de, and ce?

 

[DaveE]

Depending upon what angles you did measure, you should be able to reconstruct the light path through the prism in terms of the unknown index of refraction. The algebra may not be trivial.

Can you provide details about the prism and what data you collected? A diagram would be good.

Yes, you should be able to solve this by breaking it down into two refraction problems with unknown angles inside the prism. You will need to know the angle between the two prism surfaces to find the angle of incidence on the 2nd surface. However, the math will be messy. You may need to do a numerical solution.

 

[Jane Smith]

Do you have measurements for the distances bc, de, and ce?

Yes, I do

 

[Jane Smith]

Yes, you should be able to solve this by breaking it down into two refraction problems with unknown angles inside the prism. You will need to know the angle between the two prism surfaces to find the angle of incidence on the 2nd surface. However, the math will be messy. You may need to do a numerical solution.

I am sorry but I don't understand. That might be too advanced for me.

 

[gneill]

Do you have the apex angle of the prism?

 

[DaveE]

Draw a picture and name every angle of refraction at the two interfaces. Then apply Snell's law to get two formulas relating these angles to the refractive indicies. You can also make an equation that relates the internal angles and the angle of the prism surfaces. You will know 3 of the 5 angles (prism, entry, and exit) and the index of refraction in air. But, you don't know the internal angles, so you will need to work with the equations to eliminate them.

 

[Jane Smith]

Do you have the apex angle of the prism?

The apex angle is 60 degrees.

 

[DaveE]

So, 3 equations, 3 unknowns...