Embedded Files
Abstract
Abstract
IMG_2367.MOV
Introduction
Introduction
Have you ever noticed that objects appear to “bend” or change shape in water? This phenomena, known as refraction, is largely due to the fact that light travels at different speeds in different mediums. Discovered in 1621 by Dutch astronomer and mathematician Willebrord Snell, the law of refraction, or Snell’s law, has long been a cornerstone of how physicists understand the way light interacts with other mediums. This law is important because it relates the refractive indexes of light passing through different mediums, which are measures of the bending of a light ray when passing from one medium to another. More specifically, the refractive index is the ratio of the velocity of light in a vacuum to the velocity of light in another substance.
Background
Background
In working on this experiment, an understanding of refraction and temperature was necessary. Firstly, the index of refraction is a measure of the bending of a ray of light when passing from one medium into another. To calculate the index of refraction, two angles must first be measured: the angle of incidence, and the angle of refraction. The angle of incidence of a ray in vacuum is the angle between the incoming light ray and the line perpendicular to the surface of a medium. On the other hand, the angle of refraction of light is the angle between the light ray in the medium and the line perpendicular to the surface of a medium inside the medium.
These two angles are necessary components of Snell’s Law, which states that n1sinϴ1 = n2sinϴ2, where n1 is the index of refraction of air (which is 1.0003, or ≈1), ϴ1 is the angle of incidence, ϴ2 is the angle of refraction, and n2 is the refractive index of the water.
Next, we researched the relationship between temperature and the index of refraction, which had to be done in a somewhat roundabout manner by relating temperature to volume, volume to density, and density to the light refractive index. Thus, we used Charles’s Law, the density equation, and the Gladstone-Dale relation. Firstly, Charles’s Law states that temperature is directly proportional to volume, so when temperature increases, volume does as well. The density equation (ρ=m/V) gives us the fact that density (ρ) is inversely proportional to volume, so when volume (V) increases, density decreases. Lastly, the Gladstone-Dale relation (ρ=K(n-1)) reveals that density is directly proportional to the light refractive index (n). By researching these three formulae, we were able to come up with a relationship between temperature and the light refractive index which will be addressed in the Theoretical Work section. (Important Note: though these equations are mainly meant for gasses such as air, they are applicable to water.)
Materials and Methods
Materials and Methods
For this experiment, the light refractive index of a high-powered laser pointer was measured using a rectangular plastic container filled with water of varying temperatures.
Materials Used:
A high powered laser pointer
A rectangular plastic container
A hot plate
The Logger Pro application with accompanying temperature probe
Computer
A stand for the laser pointer to point downwards at a given angle
Protractor
A 400ml glass beaker
First, to conduct the experiment, a stand was created in order to allow the laser pointer to point downwards at an appropriate angle. For the experiment, the chosen incidence angle was 32 degrees, but any angle that could shine down through the water surface would also be acceptable. Then, the laser pointer was duct taped to the stand so that it could stay in place during the experiment. Next, a 400ml glass beaker was filled with 400ml of water, before being placed on a hot plate and heated to 70℉, measured using the temperature probe connected to the Logger Pro application on a computer. (Fahrenheit was used instead of Celsius due to the ease of using smaller increments in temperature increase, as heating with the hot plate took a very long time.)
Once the glass beaker was heated to 70℉, it was then poured into the rectangular plastic container, positioned so that the light from the laser pointer would hit relatively near one of the sides parallel to it. Afterwards, a protractor was used to measure the angle of the light beam in the water, from where it touched the bottom of the container to where it entered the water’s surface (for our experiment, a paper protractor was made in order to better calculate the angle, as the normal protractors did not precisely measure from ground level correctly.) Once this angle was taken, we subtracted it from 90° to get the correct angle of refraction. This phase occurred quickly in order to preserve the temperature of the water.
Lastly, the water was poured out and the container was dried before filling a new 400ml of water into the 500ml glass beaker and repeating the previous steps for three trials each of 70℉, 75℉, 80℉, 85℉, and 90℉ temperature water.
The paper protractor
How it worked
Theoretical Work
Theoretical Work
In the background section, we learned that Charles’s Law states that temperature is directly proportional to volume. We also learned from the density equation that density is inversely proportional to volume. By combining these two equations, we get that temperature is inversely proportional to density, as when temperature increases, volume increases, and as volume increases, density decreases.
In addition, (from the background section) the Gladstone-Dale relation shows that density is directly proportional to the light refractive index. Combined with the previous fact that temperature has an inverse relationship with density, we get that temperature has an inverse relationship with the light refractive index, as when temperature increases, density decreases, and as density decreases, the light refractive index decreases. As a result of the combination of these formulae, we ultimately hypothesized that temperature would be inversely proportional to the light refractive index in this experiment, meaning that as we increased the temperature, the light refractive index of the water would decrease.
Results
Results
Results, Calculations:
Finding the Index of Refraction:
ϴ1 = incidence angle = 32°
ϴ2 = refraction angle = 23.66°
Equation: sin ϴ1 / sin ϴ2 = Index of Refraction
sin (32°) / sin (23.66°) = 1.320
Discussion, Analysis, and Uncertainty
Discussion, Analysis, and Uncertainty
As shown in figures 5 and 6, the data from this experiment does support our original hypothesis that temperature and the light refractive index have an inverse relationship, as when temperature increased, the light refractive index decreased. As the graph reflects, the R squared value of the best fit line of the graph is 0.9759, which shows that the correlation between the two variables measured is extremely strong.
However, certain sources of uncertainty could have been removed in order to make the calculations even more precise. For example, using a more precise measurement than a protractor, as sometimes the angle of the refraction was between the individual degrees. Another such example would be using a larger container with more water to obtain a greater variance in angle measure, and thus a more precise determination of a relationship between the two variables, as all of the angles were relatively close in this experiment. However, the uncertainty wasn’t too great as the data was consistent with the background theory and hypothesis.
Conclusion
Conclusion
IMG_2029.MOVSources
Sources
Refractive Index Explanation
Refraction and Snell’s Law Explained
An explanation of why light refracts
And https://www.sciencelearn.org.nz/resources/49-refraction-of-light#:~:text=light%20in%20water-,When%20light%20travels%20from%20air%20into%20water%2C%20it%20slows%20down,more%20towards%20the%20normal%20line.
Snell’s Law Explained https://www.physicsclassroom.com/class/refrn/Lesson-2/Snell-s-Law
Gladstone-Dale relation https://www.chemeurope.com/en/encyclopedia/Gladstone-Dale_relation.html
Ideal Gas Law Density http://www.molecularsoft.com/help/Gas_Laws-Ideal_Gas_with_Density.htm
Density Volume Equation https://sciencing.com/convert-volume-density-5822298.html
Snell’s Law Image https://www.google.com/search?q=snell%27s+law&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjDtpqCrJb3AhUHk4kEHdoBC9cQ_AUoAXoECAIQAw&biw=1440&bih=789&dpr=2&safe=active&ssui=on#imgrc=tR5kC8Zs_5Dp6M
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