refractive index of sugar solution experiment

Figure 1: The sugar solution causes the laser light to bend, and the mirror reflects the light upward.

Figure 2: the sugar solution bends the laser light, and the mirror reflects the light. a mirror image can also be seen., explanation.

The Index of Refraction is defined by Snell's Law which is:

Where 'n' is the index of refraction, and theta (θ) is the angle from the normal.

Figure 3: Light will bend through a change in medium, as well as reflect. θ 1 and θ 2 represent the index of refraction.

In this demonstration, the sugar water is not evenly distributed. There is a higher concentration, about 80% sugar at the bottom while there is nearly pure water near the top. The index of refraction for 80% sugar solution is known to be about 1.5, while water is 1.33. The index of refraction (n) is a number with no units.

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Refractive index as a function of concentration of sugar solution and wavelength of light

We recently performed an experiment with the idea to find refractive index of medium (water) as a function of wavelength of light. We then added some sugar to see how the refractive index changes with concentration of sugar solution. We got the following graphs.

Are the relationships actually linear? Or are these just limiting cases? Can someone shed some intuition on why the graph is in the way it is?

• visible-light

• 2 $\begingroup$ You seem to be missing uncertainty bars on your data points ;-). Those will tell you a lot about how much you can trust that linear dependence. $\endgroup$ –  Emilio Pisanty Commented Jul 20, 2017 at 7:43
• $\begingroup$ For the relation $n=f(\lambda)$, Cauchy's law may be what you're looking for ($n = A + \frac{B}{\lambda^2} + \dots$). For the relation $n = f(c)$, you may see this paper . $\endgroup$ –  Spirine Commented Jul 20, 2017 at 7:50
• $\begingroup$ @Spirine: Thank you for the Cauchy's law. But that paper doesn't have any explanation on why its linear. $\endgroup$ –  Razor Commented Jul 20, 2017 at 13:06
• $\begingroup$ The graph is approximately hyperbolic. Hyperbola graphs are approximately linear near the asymptotes. $\endgroup$ –  Yashas Commented Jul 20, 2017 at 14:48
• 1 $\begingroup$ @Yashas That's a fairly misleading characterization, I should think. Cauchy's law is a useful approximation in some regimes but nothing more than that, and once you get to where it would get properly 'hyperbolic', you find that the model breaks down. Instead, a much more useful characterization is as a sum of Lorentz oscillators (which are also approximately linear when you're far enough from the resonance). $\endgroup$ –  Emilio Pisanty Commented Jul 20, 2017 at 15:22

For the dependence on the sugar concentration you do expect from first principles (at least at low saturations) that the dependence will be linear, since the electric susceptibility $\chi$ is essentially the molecular polarizability $\alpha$ of each contributing species times the number density of said species.

As far as the wavelength dependence goes, it's not fully linear but it's a good approximation over that range. (And, as I mentioned in the comments, your data looks vaguely linear but once you put in the error bars and do a full uncertainty analysis, you're likely to find that it's much more consistent with a variety of non-linear behaviours than it looks from your graph.) This website has some reasonable-looking data, and this is backed up in the literature:

Refractive Index of Water and Its Dependence on Wavelength, Temperature, and Density. I. Thormählen, J. Straub, and U. Grigull. J. Phys. Chem. Ref. Data 14 , 933 (1985) , NIST eprint .

In particular, if you look for wavelengths just a bit above and below that range, you get something much more illuminating,

i.e. the downward slant comes because the visible range is sandwiched between two resonances, which themselves can be well described using the Lorentz oscillator model .

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How do I find the refractive index in sugar solutions?

• Thread starter Jane Smith
• Start date Nov 3, 2018
• Tags Experiment Index Light Optics Refraction Refractive index Sugar
• Nov 3, 2018

Attachments

• Researchers discover new material for optically-controlled magnetic memory
• PhAI—an AI system that figures out the phase of x-rays that crystals have diffracted
• Achieving quantum memory in the notoriously difficult X-ray range

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.  

A PF Asteroid

Jane Smith said: 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 233369 View 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.

• Nov 4, 2018

ehild said: Do you know angle B? View attachment 233393

Jane Smith said: I do know angle B, how does this help me?

• Nov 5, 2018

gneill said: 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.

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

• Nov 6, 2018

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

DaveE said: 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.

Do you have the apex angle of the prism?  

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.  

• Nov 7, 2018

gneill said: Do you have the apex angle of the prism?

Related to How do I find the refractive index in sugar solutions?

1. what is refractive index.

Refractive index is a measure of how much a substance bends light. It is a dimensionless number that indicates the ratio of the speed of light in a vacuum to the speed of light in that substance.

2. Why is it important to measure refractive index in sugar solutions?

Measuring the refractive index in sugar solutions can provide information about the concentration and purity of the solution. It can also be used to determine the amount of sugar dissolved in a solution, which is important in industries such as food and beverage production.

3. What is the relationship between refractive index and sugar concentration?

The refractive index of a sugar solution is directly proportional to the concentration of sugar in the solution. This means that as the concentration of sugar increases, the refractive index also increases.

4. How do I measure the refractive index in sugar solutions?

The most common method for measuring refractive index in sugar solutions is using a refractometer. This instrument uses the principle of total internal reflection to determine the refractive index of a solution. It is important to calibrate the refractometer with a standard solution before use.

5. What factors can affect the accuracy of refractive index measurements in sugar solutions?

The accuracy of refractive index measurements in sugar solutions can be affected by temperature, the presence of impurities, and the type of sugar used. It is important to control these factors and use a standard protocol to ensure accurate measurements.

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Experimental Study of the Optical Rotation produced by sugar solved in water.

The aim of the experiment performed was to give an insight into the phenomena of optical rotation of monochromatic light through a polarizing filter and optical activity of sucrose and fructose samples. Malus’ Law was tested with satisfactory result, it was proved that sucrose is dextrorotatory and fructose daevorotatory.

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Sugar is part of the carbohydrate chain. One group of these carbohydrates is disaccharides. The sugar used in this study is sucrose which is formed by glucose and fructose. Sucrose has the property of rotating polarized light to the right. Thus, the level of sugar content in water can affect the refractive index in the sugar solution. Therefore, more sugar content can cause the refractive index in the sugar solution to increase. For example, the addition of sugar at 37.5% level can increase the refractive index from 1.333 to 1.402. As the index of refraction increases in the sugar solution, more light is absorbed. Absorption of light in a sugar solution can change the color of light from yellow (589 nm) to green (560 nm). Yellow light can be used for healthy skin and green light can be used to reduce the intensity of migraine.

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Analyses of Concentration and Wavelength Dependent Refractive Index of Sugar Solution Using Sellmeier Equation

Misto 1 , Endhah Purwandari 1 , Supriyadi 1 , Artoto Arkundato 1 , Lutfi Rohman 1 and Bowo Eko Cahyono 1

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1825 , 10th International Conference on Physics and Its Applications (ICOPIA 2020) 26 August 2020, Surakarta, Indonesia Citation Misto et al 2021 J. Phys.: Conf. Ser. 1825 012030 DOI 10.1088/1742-6596/1825/1/012030

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1 Department of Physics, Faculty of Mathematics and Natural Sciences, University of Jember Jalan Kalimantan 37, Jember 68121, Indonesia

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The concentration and wavelength-dependent refractive index of sugar solution have been determined using Sellmeier Equation. The equations describe the refractive index as a function of wavelength parameter. They could be generalized as a function of material concentration by investigating the characteristic of their Sellmeier constants A and B. The three wavelengths used to identify the refractive index of sugar solutions were 455 nm, 525 nm, and 633 nm, while the concentration of the sugar solution ranged from 0 to 40%. This paper reported in this research performed the empirical expression of concentration-dependent of the sugar solution. The A and B Sellmeier constants were the main subjects to be concerned. A constant has a linear relationship with the sugar solution at 15% concentration to 40%. Under a concentration of 15%, the refractive index is quadratic towards engagement. The sellmeier B constant has a quadratic relation characteristic below the attention of 15%. Above 15%, the constant B and concentration of sugar solution were associated with the 4th order polynomial equation.

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