# Ask an Expert: Measuring Sugar Content of a Liquid with a Laser Pointer

**Moderator:** kgudger

### Measuring Sugar Content of a Liquid with a Laser Pointer

Hello, Im thinking of doing this project for my presentation but im trying to understand how does the project work before purchasing the kit or bulding it. I cant figure out where would the Graduated cylinder go, where should the liquide go etc., I also dont understand the formula's(haven't seen them in classe).. I am in secondary 5 and my project is due in approximatelly on month. Someone please help me. I'll really appreciate that.

Thanks

Thanks

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

Hi ali53481,

The graduated cylinder is used to make the standard sugar solutions. It doesn't get used in the part of the experiment where you are actually measuring how the laser beam is refracted by the solutions in the prism. The liquids are added to the prism by pouring them through the hole in the top of the prism. You can see the hole in Figures 7 and 8 of the procedure.

Is there a particular equation that you are having trouble understanding? The first thing to do is read through the background section of the project very carefully. Then, read the three references listed in the Bibliography section. If you still have questions, please post back with them and we'll answer them. The more detailed your questions are, the easier it will be to help you.

The graduated cylinder is used to make the standard sugar solutions. It doesn't get used in the part of the experiment where you are actually measuring how the laser beam is refracted by the solutions in the prism. The liquids are added to the prism by pouring them through the hole in the top of the prism. You can see the hole in Figures 7 and 8 of the procedure.

Is there a particular equation that you are having trouble understanding? The first thing to do is read through the background section of the project very carefully. Then, read the three references listed in the Bibliography section. If you still have questions, please post back with them and we'll answer them. The more detailed your questions are, the easier it will be to help you.

All the best,

Terik

Terik

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

thankyou for your quuick reply,

I still have a couple of question, your first reply helped a lot

In equation 1(n1 sin θ1= n2 sin θ2) what are we searching or trying to isolate ? is it ''θ2 = angle of refraction (degrees or radians)''

In the procedure scetion and I mesure X and L on my monitore and did the arctangente and then i applied it to the formula and got an index of refraction of solution of 1.76. Is that correct ?(I know it said not to scale, I just wanted an approximation)

once i get the index of refraction of solution of the water, what do i do with it, DO a compare it to the index of refraction of solution with sugar or what ?

and should I really by the kit on the website, I got a powerful laser Graduated cylinder, 100 mL, Stir rod, plastic, 12 inches. I only dont have the triangle prism. Is it easy to build or should I buy the kit only for this item ?

thanks a lot for your help.

I still have a couple of question, your first reply helped a lot

In equation 1(n1 sin θ1= n2 sin θ2) what are we searching or trying to isolate ? is it ''θ2 = angle of refraction (degrees or radians)''

In the procedure scetion and I mesure X and L on my monitore and did the arctangente and then i applied it to the formula and got an index of refraction of solution of 1.76. Is that correct ?(I know it said not to scale, I just wanted an approximation)

once i get the index of refraction of solution of the water, what do i do with it, DO a compare it to the index of refraction of solution with sugar or what ?

and should I really by the kit on the website, I got a powerful laser Graduated cylinder, 100 mL, Stir rod, plastic, 12 inches. I only dont have the triangle prism. Is it easy to build or should I buy the kit only for this item ?

thanks a lot for your help.

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

Hi ali53481,

In equation 1, you usually know the index of refraction of the first material (n1) and angle of incidence (θ1). Depending on the problem, you usually know either n2 or θ2. In this project, the goal is to determine the index of refraction of the second material, n2. So, n1, θ1, and θ2 are the known values. You will solve for n2. Equations 2, 3, 4, and 5 each have the goal of solving for n2 based on the refraction of a laser beam through an equilateral triangular prism. In those equations, however, n takes the place of n2 and n_air takes the place of n1 in equation 1.

I measured X and L on my monitor and got a number very, very close to 1.76. You used the formula correctly.

The index of refraction of the water solution is a control to make sure your experiment is working correctly. If you make all the measurements with water in the prism and get a number close to 1.334, then your experiment is working. If you do not get a number close to 1.334, then something is set up incorrectly and you should double check your setup.

If you have all of the other materials, you will probably find it less expensive to buy a hollow triangular prism separately. Just make sure that the prism is equilateral, triangular, and hollow. You can also try to make a prism out of microscope slides, but that can be a finicky process.

In equation 1, you usually know the index of refraction of the first material (n1) and angle of incidence (θ1). Depending on the problem, you usually know either n2 or θ2. In this project, the goal is to determine the index of refraction of the second material, n2. So, n1, θ1, and θ2 are the known values. You will solve for n2. Equations 2, 3, 4, and 5 each have the goal of solving for n2 based on the refraction of a laser beam through an equilateral triangular prism. In those equations, however, n takes the place of n2 and n_air takes the place of n1 in equation 1.

I measured X and L on my monitor and got a number very, very close to 1.76. You used the formula correctly.

The index of refraction of the water solution is a control to make sure your experiment is working correctly. If you make all the measurements with water in the prism and get a number close to 1.334, then your experiment is working. If you do not get a number close to 1.334, then something is set up incorrectly and you should double check your setup.

If you have all of the other materials, you will probably find it less expensive to buy a hollow triangular prism separately. Just make sure that the prism is equilateral, triangular, and hollow. You can also try to make a prism out of microscope slides, but that can be a finicky process.

All the best,

Terik

Terik

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

thanks a lot for youre help, if I have any further question, I will reply to you

Thank You

Thank You

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

Hi again, Sorry to bother you but im a bit lost, do you actually need the equation 1 because they are comparing air to water ? an how is θ2 a known value, and if where searching for n2 why are we searching for it again in equation 2,3,4 and 5

and if I understand correctly equation 5 is the simplefication of equation,2,3,4 ?

Thanks again for your help

and if I understand correctly equation 5 is the simplefication of equation,2,3,4 ?

Thanks again for your help

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

Hi ali53481,

I'm sorry for the delay in responding to you! Usually I get an email when you make a post, but I didn't this time. I will check my notification settings.

Equation 1 is true for light refracting between any two media--water and air, water and oil, oil and glass, glass and quartz, etc. This equation is the basis for all other equations in this project.

You are correct that equation 5 is a simplification of equations 2, 3, and 4. Equation 2 comes from applying equation 1 to the prism.

In this project, the equations 2, 3, and 4 walk you through some simplifications that get you from equation 1 to equation 5. You are searching for n2 because n2 (the index of refraction of the liquid in the prism) is what you will use to determine the sugar content of the liquids you test.

Post back if you have other questions!

I'm sorry for the delay in responding to you! Usually I get an email when you make a post, but I didn't this time. I will check my notification settings.

Equation 1 is true for light refracting between any two media--water and air, water and oil, oil and glass, glass and quartz, etc. This equation is the basis for all other equations in this project.

You are correct that equation 5 is a simplification of equations 2, 3, and 4. Equation 2 comes from applying equation 1 to the prism.

In this project, the equations 2, 3, and 4 walk you through some simplifications that get you from equation 1 to equation 5. You are searching for n2 because n2 (the index of refraction of the liquid in the prism) is what you will use to determine the sugar content of the liquids you test.

Post back if you have other questions!

All the best,

Terik

Terik

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

Hi again , I have an other question. (youve been a great help by the way ). My project is almost done (Measuring Sugar Content of a Liquid with a Laser Pointer) but I still dont understand a couple of things.

I build my own hollow prism with microscope slide, so when I compare the sugar to the water, there isn't much difference where the laser beam goes on the cart board (or wall) there is only about 1cm of difference, is that normal ?

And my other question is what do I do when I find the index of refraction of solution(with sugar) ? (do I compare it to the index of refraction of water)

-thanks a lot for your help

I build my own hollow prism with microscope slide, so when I compare the sugar to the water, there isn't much difference where the laser beam goes on the cart board (or wall) there is only about 1cm of difference, is that normal ?

And my other question is what do I do when I find the index of refraction of solution(with sugar) ? (do I compare it to the index of refraction of water)

-thanks a lot for your help

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

For the index of refraction of water, I got 1.400555958. The theoretical value is about 1.334. Is that a big deal ? should I be more precise ? thanks

### Re: Measuring Sugar Content of a Liquid with a Laser Pointer

Hi ali53481,

I'm glad to hear your project is progressing well! Your measurement for the index of refraction is farther off than I would expect. A value between 1.32 and 1.34 would be typical from this experimental setup. Do you get this same value if you redo the experiment? Have you double checked your calculations to make sure you are using consistent units and following the correct order of operations? It's possible that if you built your own prism the angles might not be exactly 60/60/60 degrees. If so, that would affect the accuracy of your measurements. The good news is that even if you don't measure the index of refraction of pure water accurately, you can still successfully measure the sugar content of a liquid with the laser pointer as long as you measure precisely. This website has a nice explanation of the difference between accuracy and precision: http://www.mathsisfun.com/accuracy-precision.html.

The laser beam won't move very far. If you want it to move farther, you can put the prism farther from the wall. Just make sure that the prism is the same distance from the wall for all of your measurements.

As far as what to do with data goes, you should make a graph that has index of refraction, n, on the x-axis and sugar content on the y-axis. Plot the indices of refraction and sugar contents of the pure water (sugar content = 0%) and three standard sugar solutions (10%, 20%, 30%) on this graph. To measure the sugar content of an unknown liquid, like apple juice, measure the index of refraction of the unknown liquid. Then, compare the index of refraction with your graph to estimate the sugar content of the unknown by interpolating between the data points for the pure water and standard sugar solutions.

I'm glad to hear your project is progressing well! Your measurement for the index of refraction is farther off than I would expect. A value between 1.32 and 1.34 would be typical from this experimental setup. Do you get this same value if you redo the experiment? Have you double checked your calculations to make sure you are using consistent units and following the correct order of operations? It's possible that if you built your own prism the angles might not be exactly 60/60/60 degrees. If so, that would affect the accuracy of your measurements. The good news is that even if you don't measure the index of refraction of pure water accurately, you can still successfully measure the sugar content of a liquid with the laser pointer as long as you measure precisely. This website has a nice explanation of the difference between accuracy and precision: http://www.mathsisfun.com/accuracy-precision.html.

The laser beam won't move very far. If you want it to move farther, you can put the prism farther from the wall. Just make sure that the prism is the same distance from the wall for all of your measurements.

As far as what to do with data goes, you should make a graph that has index of refraction, n, on the x-axis and sugar content on the y-axis. Plot the indices of refraction and sugar contents of the pure water (sugar content = 0%) and three standard sugar solutions (10%, 20%, 30%) on this graph. To measure the sugar content of an unknown liquid, like apple juice, measure the index of refraction of the unknown liquid. Then, compare the index of refraction with your graph to estimate the sugar content of the unknown by interpolating between the data points for the pure water and standard sugar solutions.

All the best,

Terik

Terik

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