1:45 PM - 3:15 PM
[O08-P91] Experiment and Analysis of Mirage Reproduction using Solution Concentration Gradient
Keywords:Mirage, light trajectory, reproduction experiment, sucrose solution
1 Introduction
A mirage is an atmospheric optical phenomenon in which an object appears as an inverted or distorted false image due to the refraction of light caused by the gradient of refractive index in the air. The distance between the observer and the real image and the atmospheric conditions, such as temperature distribution and wind, must meet certain conditions for the occurrence of mirages. The cause of mirages in these locations is that water and asphalt heat up and cool down differently from air.
The refractive index of air varies mainly with temperature. There are few cases in which the trajectory of light at the time of mirage occurrence has been accurately illustrated by theoretical calculations (Shibata 2013). Another previous study was conducted by the Natural Science Physics Group of Shimizu Higashi High School in Shizuoka Prefecture (2009). This study illustrated the trajectory of light when reproduced experimentally. However, because the method was not a theoretical calculation, it could not be applied to calculations under changing conditions. Therefore, we conducted this study with the goal of accurately illustrating the trajectory of light in a mirage based on theoretical calculations. In this study, the trajectory of light in a mirage was drawn on Excel and compared with the trajectory of light in a reproduced experiment using sucrose solution. There are three types of mirages: upper mirages, lower mirages, and lateral mirages. In this reproduction experiment and analysis, we focused on the upper mirage.
2 Research method
Reproduction experiment
(1) Eight aqueous sucrose solutions (0, 8, 16, 24, 31, 37, 44, and 50% by weight) were prepared so that the refractive indices were equal between 1.33 and 1.42.
(2) Gently pour the sucrose solutions into the bottom of the tank using a syringe, starting from the one with the lowest refractive index, to create a tank of eight layers of sucrose solutions of the same thickness.
(3) A green laser beam is incident at an angle from the bottom layer. The angle of incidence was increased by 5 degrees from 5 degrees to the side of the tank until total reflection of the light on the surface of the water occurred.
(4) Measure the coordinates after the laser light is refracted. The angle was measured by attaching a smartphone to the side of the laser pointer.
3 Analysis
Assuming that a section is divided into multiple layers, each layer has a different refractive index, and the refractive index is gradational. Using Excel, we calculate the angular change of light due to refraction and the distance traveled between each layer. The calculated results are used to plot the trajectory of the light. In addition, the coordinates after the refraction of the light are clarified in order to compare with the previous reproduction of the experiment.
The calculations were performed using Snell’s law. Theoretically, the light becomes horizontal at the top of its trajectory. Therefore, the calculation was divided into two parts, one from the light incidence until the light becomes horizontal, and the other after the light becomes horizontal, and they were combined at the stage shown in the figure.
4 Results and Discussion
Compared to the experiment in which the light was reproduced, the analysis showed a greater degree of bending of the light. In the experiment, the distribution of the refractive index was not constant, but in the analysis, it was assumed that the refractive index was always constant. From this, it was considered that the distribution of the refractive index was related to the light bending. In the analysis, the number of layers was assumed to be extremely multilayered, but when the number of layers was small, the curvature of the light was clearly small. As the number of layers was increased, the curvature of the light became larger. This can also be attributed to the difference in the distribution of the refractive index.
5 References
Shibata, K., 2013: Multi-image mirage in a stable stratosphere: Possibility of ray tracing and temperature structure estimation. Weather, 60, 709-722
Physics Group, Shimizu Higashi High School, Shizuoka, Japan, 2009: Analysis of mirage model by ray tracing. 53rd Japan Student Science Award
A mirage is an atmospheric optical phenomenon in which an object appears as an inverted or distorted false image due to the refraction of light caused by the gradient of refractive index in the air. The distance between the observer and the real image and the atmospheric conditions, such as temperature distribution and wind, must meet certain conditions for the occurrence of mirages. The cause of mirages in these locations is that water and asphalt heat up and cool down differently from air.
The refractive index of air varies mainly with temperature. There are few cases in which the trajectory of light at the time of mirage occurrence has been accurately illustrated by theoretical calculations (Shibata 2013). Another previous study was conducted by the Natural Science Physics Group of Shimizu Higashi High School in Shizuoka Prefecture (2009). This study illustrated the trajectory of light when reproduced experimentally. However, because the method was not a theoretical calculation, it could not be applied to calculations under changing conditions. Therefore, we conducted this study with the goal of accurately illustrating the trajectory of light in a mirage based on theoretical calculations. In this study, the trajectory of light in a mirage was drawn on Excel and compared with the trajectory of light in a reproduced experiment using sucrose solution. There are three types of mirages: upper mirages, lower mirages, and lateral mirages. In this reproduction experiment and analysis, we focused on the upper mirage.
2 Research method
Reproduction experiment
(1) Eight aqueous sucrose solutions (0, 8, 16, 24, 31, 37, 44, and 50% by weight) were prepared so that the refractive indices were equal between 1.33 and 1.42.
(2) Gently pour the sucrose solutions into the bottom of the tank using a syringe, starting from the one with the lowest refractive index, to create a tank of eight layers of sucrose solutions of the same thickness.
(3) A green laser beam is incident at an angle from the bottom layer. The angle of incidence was increased by 5 degrees from 5 degrees to the side of the tank until total reflection of the light on the surface of the water occurred.
(4) Measure the coordinates after the laser light is refracted. The angle was measured by attaching a smartphone to the side of the laser pointer.
3 Analysis
Assuming that a section is divided into multiple layers, each layer has a different refractive index, and the refractive index is gradational. Using Excel, we calculate the angular change of light due to refraction and the distance traveled between each layer. The calculated results are used to plot the trajectory of the light. In addition, the coordinates after the refraction of the light are clarified in order to compare with the previous reproduction of the experiment.
The calculations were performed using Snell’s law. Theoretically, the light becomes horizontal at the top of its trajectory. Therefore, the calculation was divided into two parts, one from the light incidence until the light becomes horizontal, and the other after the light becomes horizontal, and they were combined at the stage shown in the figure.
4 Results and Discussion
Compared to the experiment in which the light was reproduced, the analysis showed a greater degree of bending of the light. In the experiment, the distribution of the refractive index was not constant, but in the analysis, it was assumed that the refractive index was always constant. From this, it was considered that the distribution of the refractive index was related to the light bending. In the analysis, the number of layers was assumed to be extremely multilayered, but when the number of layers was small, the curvature of the light was clearly small. As the number of layers was increased, the curvature of the light became larger. This can also be attributed to the difference in the distribution of the refractive index.
5 References
Shibata, K., 2013: Multi-image mirage in a stable stratosphere: Possibility of ray tracing and temperature structure estimation. Weather, 60, 709-722
Physics Group, Shimizu Higashi High School, Shizuoka, Japan, 2009: Analysis of mirage model by ray tracing. 53rd Japan Student Science Award