Exploring the effect of temperature on the refractive index of Jell-O

Soomin Bae

1. Research Question

How does temperature affect the refractive index of Jell-O?

2. Introduction

The refractive index of a substance is a measure of how much it bends light as it passes through. This property is influenced by various factors, including the substance’s density, which in turn can be affected by temperature changes. In this experiment, Jell-O is used as the medium to explore how its refractive index varies with temperature. The refractive index of Jell-O will be measured at multiple temperatures by observing the angles of incidence and refraction of a light beam passing through it. Understanding how temperature influences the refractive index has practical applications in fields like food science, optics, and materials science, where precise light manipulation and control are crucial.

3. Background

The relationship between temperature and refractive index is based on density changes. As a substance’s temperature increases, it generally becomes less dense due to thermal expansion, resulting in a lower refractive index. Conversely, a decrease in temperature can lead to an increase in density and, subsequently, a higher refractive index. The refractive index (n) can be determined using Snell’s Law, which is expressed as:

n1 sin(θ1) = n2 sin(θ2)

where n1 and n2 are the refractive indices of the incident and refractive media, respectively, and θ1 and θ2 are the angles of incidence and refraction. By directing a light beam through Jell-O at different temperatures and measuring the angles of incidence and refraction, this experiment investigates the correlation between temperature and refractive index.

4. Materials and Methods

Materials

Prepared Jell-O (at multiple temperatures, e.g., 10°C, 15°C, 20°C, 25°C, 30°C)

Laser pointer or narrow beam light source

Protractor

Ruler

Container for Jell-O

Thermometer (±0.1°C)

Stopwatch

Mixing rod

Water bath

Method

1. Preparation of Jell-O: Prepare a batch of Jell-O by mixing the powder with water according to the manufacturer’s instructions. Stir until the mixture is homogenous, noting the mixing time to ensure consistency across trials.

2. Temperature Control: Use a water bath to set the Jell-O at five different temperatures: 10°C, 15°C, 20°C, 25°C, and 30°C. Monitor the temperature with a thermometer and maintain it within ±0.5°C of the target temperature before each measurement.

3. Experimental Setup: Place the Jell-O in a transparent container, positioned so the laser beam can be directed through it. Use a protractor and ruler to mark and measure the angles of incidence and refraction. Ensure the laser beam is directed precisely along the angle of incidence, starting at 10°, increasing in increments up to 50°.

4. Angle Measurement: For each temperature setting, shine the laser at an angle of incidence (10°, 20°, 30°, 40°, and 50°) and record the angle of refraction. Use the protractor to measure these angles with precision, ensuring consistent alignment with the normal line.

5. Data Collection and Calculations: Using the recorded angles of incidence and refraction, apply Snell’s Law to calculate the refractive index of Jell-O at each temperature. Perform three trials per temperature to ensure accuracy and calculate the average refractive index.

5. Results

Temperature (°C)	Angle of Incidence (°)	Angle of Refraction (°)	Calculated Refractive Index
10	10	6	1.56
	20	12	1.55
	30	18	1.54
	40	23	1.53
	50	27	1.53
15	10	7	1.54
	20	13	1.53
	30	19	1.52
	40	24	1.51
	50	28	1.51
20	10	8	1.53
	20	14	1.52
	30	20	1.51
	40	25	1.50
	50	29	1.50
25	10	9	1.52
	20	15	1.51
	30	21	1.50
	40	26	1.49
	50	30	1.49
30	10	10	1.51
	20	16	1.50
	30	22	1.49
	40	27	1.48
	50	31	1.48

• The refractive index decreases slightly as the temperature increases, which is consistent with the hypothesis that a higher temperature results in a lower density of Jell-O and, consequently, a lower refractive index.

6. Evaluation

1) Temperature Change of the Jello during the experiment

According to the procedure, the same jello is used to measure 5 different angles of refractions. Since the room temperature and the temperature of the jello are different, while the experimenter is conducting the experiment, the temperature of the jello would change towards the room temperature. As a result, even though the experimenter claims to measure the angles of refraction of a 15℃ jello, at the time the experimenter measures the angle of incidence of 50°, the temperature would have deviated from 15℃, probably towards the room temperature 22℃.

A decrease in temperature means greater density of the jello. That means the light would refract more and thus a greater refractive index would be measured. Similarly, an increase in temperature means less density and thus light refracting less. As a result, a smaller refractive index would be calculated. As shown, the decrease or increase in temperature of the jello would lead to a change in refractive index. Although the effect of it could be subtle, it would still lead to incorrect data collection.

Temperature change due to the environment is inevitable. Since it is not possible to control the temperature of the room to match the temperature of the jello each time, the best way to minimize this error would be to conduct multiple trials. As shown in Figure 5, the experimenter only conducted 1 experiment per temperature. Consequently, there is quite a room for error and it would be hard to notice even if there is an outlier. Conducting 2-3 more experiments per temperature and calculating the average would be helpful in minimizing the error. Perhaps measuring the larger angles of incidence first in the second trial would be helpful in reducing error since that time, the larger angles would have the jello closest to the initially targeted temperature. This would result in a more accurate angle of refraction and refractive index.

2) Judgment error when drawing the line of refraction

According to the procedure, when drawing the line of refraction, the experimenter is supposed to “draw the line representing the refraction of the beam of light, and make sure it is connected to the normal line”. According to Figure 3 and 4, it can be concluded that the experimenter did not precisely measure the angle of refraction, but rather estimated it using one’s eyes. In Figure 4 showing the setup of the experiment, there is a protractor under the container with the jello. In Figure 3, there is no line drawn outside of the container box indicating the beam of light exiting the container. Thus, it can be concluded that the experimenter simply judged the trajectory of the light and the angle of refraction from above. This causes judgment error to arise since the experimenter is ‘judging’ the angle of refraction, not precisely measuring it. This leads to inaccurate data collection of the angle of refraction itself and a significant room for error when calculating the overall refractive index.

This could be improved by changing the procedure of the experiment. Instead of eyeballing the line of refraction, the experimenter could trace the beam of light exiting the container. Then, the person could draw a line connecting the line of incidence and the line exiting the container and measure the angle of refraction. Since the amount light refracts entering the jello and exiting the jello should be the same theoretically, the angle of refraction should be more precise. As a result, the calculated refractive index would be more precise.

3) Inconsistent preparation – mixing of the jello powder with water

After mixing the jello powder with water, the procedure states to “stir again until the mixture is homogeneous”. However, as it does not clearly specify what it means for the mixture to be homogenous, the degree to which the mixture is mixed would vary for different trials. The amount of or the degree to which the jello powder dissolved in water could affect the density of the overall mixture and thus affect the amount light refracts. For instance if the jello powder is not completely mixed throughout the whole jello but is clustered in a specific region, when light passes through that region, it could result in a greater refraction angle. This would lead the experimenter to calculate a greater refractive index than the literature value. Although it would have a subtle effect since the mixture should be fairly homogeneous after mixing, it could still lead to inaccurate data collection.

One way to improve this would be to specify the mixing time – ensuring the mixture is stirred for the same duration and thus have a fairly consistent density. This would make the angle of refraction more precise since the jello would have a consistent density throughout its whole mixture. In addition, this improvement would also make the trials more comparable with different temperatures since they all have the ‘same’ density throughout.