# How do temperature and salt concentration effect the index of refraction of water?

Abstract: For this experiment, I intend to create a set up using a water container and laser pointer that will measure the index of refraction of water. I will do this by measuring the angle at which the light enters and exists the water. I will be varying the temperature of water as well as the salt content in order to observe whether or not it creates a measurable difference in the angle of refraction.
Refraction definition: "deflection from a straight path undergone by a light ray or energy wave in passing obliquely from one medium into another in which its velocity is different" (1).

## Guiding Question

Does the temperature and salt concentraion effect the index of refraction of water and if so, by how much?

## Hypothesis/Prediction

My prediction is that the temperature will not cause a very large difference in the index of refraction. I found results from an experiment that addressed this question and the changes were so slight that they were barely measurable (2). But in contrast to this, I read that in underwater acoustics, the amount of ray bending is dependent on the variation in temperature, salinity, and pressure of the water (3). Due to these statements, I predict that with the temperatures and salinities I will be observing there will not be a very noticeable or accurately measurable difference, but I will use the techniques and approaches available to me in order to make the most accurate measurements and observations possible.

## Experimental Procedure

1. Make a hypothesis.
2. Collect materials: semi-circle container, laser, thermometer, cardboard, hot glue.
3. Construct design: glue down semi-circle container and laser in predetermined locations on cardboard.
4. Familiarize myself with materials. Put water in container and mark where the laser hits the cardboard after traveling through the water. Measure all distances.
5. Create a LoggerPro document that has calculated columns so that after entering the length of the adjacent and opposite sides of the triangle (drawn and explained below under May 12th), the program will calculate the third side, or hypotenuse of the triangle, as well as the angle of refraction. The water's temperature and salinity are also entered into the graph data in order to have a variable to compare the angles to.
6. Conduct a series of experiments using different temperatures and salinities.
7. Collect and observe data collected from step 5.
8. Conduct any additional experiments to re-evaluate discrepancies in data or increase the range of data points.
9. Create graphs and evaluate results.
10. Conclude, compare results to hypothesis, and state findings.

## Experiment

April 28th: Experimentation to familiarize with tools and techniques
Picture 1: Container with water showing the beams of the laser which I traced onto the paper. Picture 2: Protractor showing the measurement of the incident and refracted angles to use in order to calculate the index of refraction. Picture 3: The thermometer, laser, and container used in the experiment.

The below picture shows the most recent design plan. The laser (1) and plastic water tray (2) will be glued in place on a large piece of paper. The perpendicular line (3) that runs through the flat bottom side of the tray will be pre-drawn and measured. For example, on this drawing, below the bottom edge, the line is 9.5cm and above it is 18cm. The incoming beam (4) will run through a predetermined point on the tray's flat edge and will determine the angle of incidence. The outgoing beam (5) will go out until it reaches the end of the predrawn, perpendicular line. The line documenting the route of the beam will then be connected to the perpendicular line. In addition, an upright piece of paper or cardboard will be placed along the edge of the paper near the opposite line from the refracted angle. This will allow for the more accurate placement and observation of the movement of the beam when different water temperatures and salinities are used.
Instead of measuring the angles with a protractor as I had been doing before, I will now be using the sin (opposite over hypotenuse) of the incident angle and tan (opposite over adjacent) of the refracted angle. In this way I will be able to use measurements of the lines (two of which are fixed) to calculate the angle measurements. This technique, along with glued down, fixed materials (tray and laser), the results will be more accurate from one trial to the next. This will create more accurate overall measurements that can be compared because they were found using the same set-up.

May 14th: Begin to put together base
I obtained a large piece of cardboard and drew perpendicular lines in order to place the semi-circle container in its correct location and later calculate the index of refraction. The flap of the cardboard wil be bent upward to act as a screen when observing the laser beams.

May 19th: Complete base
I glued down the semi-circle container and laser beam to the cardboard with perpendicular lines. The laser is secured at a rather large angle and the beam hits the center of the tray. This was determined by observing the reflected beam which, when through traveling through the center, reflects back at the same angle toward the laser pointer.

May 28,2010
I graphed the angles and temperatures that have been measured so far. As displayed, there seem to be some errors in the graph. The angles measured at about 41 degrees, 46 degrees, and 51 degrees Celcius seem to be lower than they should be if you compare them to the rest of the linear pattern. The differing measurements will be retested in order to determine the problem. In addition, I will test more measurements between 21 and 41 degrees Celcius in order to have a more broad and accurate collection of data.

June 2, 2010
I tested the angle of refraction of salt water. I started with 400mL of water and measured out 53 grams of salt. I used a stirring plate to mix it together. I poured the solution into the container and measured the angle. Then I added 200mL of water to 200mL of the original solution, mixed it, and measured the angle. I repeated this two more times, decreasing the salinity each time. I graphed the angle of refraction against the salinity and observed that as the salinity increases, the angle of refraction decreases.

June 10, 2010
I remeasured some of the temperatures that did not seem to match the expected linear progression of the water without salt. There are still some discrepancies in the graph but more of the results were linear. The graph can be compared to the first trials shown above on May 28th. For the most part, the graph shows that as the temperature increases the angle of refraction increases.

Below are pictures of the set-up that I used for my experimentation.

## Data/Analysis

In conducting this experiment, the final results showed that as the temperature of the water increases the index of refraction increases. In contrast, as the salinity increases the refraction index decreases. As previously stated, refraction is the bending of light as it moves from one medium into another and the velocity changes. The angle of incidence measured for this experiment was 44.31 degrees and of all the refracted angles measured, the highest was 29.45 degrees at 80 degrees Celcius with no salt. The accepted index of refraction of air is 1.0003 and for the 29.45 degree angle, the index of refraction is calculated to be 1.425. The lowest measured angle was 28.254 degrees with a salinity of 0.1325 and the calculated index of refraction for that would be 1.48. The index of refraction of water is obviously greater than that of air. The velocity is lower in water so the refracted angle is less than the incident; the medium slows down the movement of the beam so it bends in towards the normal creating a lesser angle measurement.
As the temperature of the water increased, the refraction index of non-salt water increased. My belief is that this occurs because as the temperature goes up, the molecules move faster and become more spread out which allows for the beam of light to move through the liquid easier and faster. If it can move through at a faster rate, it would not bend in towards the normal line lessening the angle as much. This would result in larger angles and a greater index of refraction.
As the salinity increased, the refraction index decreased. I think this result is similar to that explained above. The more salt in the water, the more dense it becomes so molecules are more tightly packed. This creates a harder medium for the beam of light to efficiently travel through. So, the greater the salinity, the more the light is slowed and bent toward the normal, the smaller the angle becomes, and the lesser the index of refraction is.
In the salt water results, the greatest difference between angles was only 0.751 degrees and among the non-salt water results, it was a difference of 0.894 degrees. The greatest variation in the index of refraction was from 1.48 and 1.425 with a difference of 0.055. So, yes there was a pattern and changes dependent on the temperature and salinity of water but the differences were so slight and small, that the results might not be entirely accurate.

## Conclusion

Because the temperatures and salinities I tested were within a rather small range, I am curious to know whether the experimentation of more extremes would provide more noticeable results that would still follow the pattern I observed in my trials. That would be one way to improve upon my experiment: more trials that increased the range of variables (i.e. more temperatures including very cold and very hot as well as a greater variation in salinities). Although my techniques and measurements might not have been entirely accurate, the results were helpful in creating a basic understanding of the rules of refraction. The use of graphs as a visual allowed for the pattern to be established and observed. The experiment could have been improved upon if more data had been collected to provide for a greater range of results. In addition, I noticed that when I turned on the laser pointer, the cardboard did not lie flat on the counter so as I pressed down the button to turn on the laser, the cardboard moved down changing the beam slightly. An improvement would be to build a more solid, secure base to ensure similar and accurate angle measurements. I am also interested to know how professionals measure the index of refraction of difference mediums and what kind of techniques and tools they use.

## Sources

(1) http://www.merriam-webster.com/dictionary/refraction
(2) http://www.usc.edu/CSSF/History/2004/Projects/S1502.pdf
(3) http://en.wikipedia.org/wiki/Refraction

## Acknowledgments

I'd like to thank Dr. Pasquini for all his help from designs to calculations to providing materials.
Thanks to Louis for the help in starting my experiment and suggesting things to focus on in order to get the best results.
Thank you Ryan Payne for helping me prepare my materials between trials.

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