### Reflection and refraction lab with Desmos

Laboratory eleven investigates reflection and refraction. The reflection component of the laboratory investigates the relationship between the object distance and image distance for a plane mirror. The refraction component uses apparent depth to determine the index of refraction for water.

Working as a team, a pair of students determines the apparent image location behind a mirror tile. This laboratory appears to have an odd twist. If the students expect that the distances are equal, they tend to wind up with measurements that support equal distances. The graph of the image distance versus the object distance has a slope of one.

If the students expect that the image distance is less than the object distance, then they appear to make measurements that support that expectation. In most terms the students predict equality of the distances and find support for that. Every few terms a student will first propose inequality prior to the laboratory and data will be found to support that inequality. Sample sizes are too small and data has not been tracked to prove that this occurs reliably.

In the refraction portion of the laboratory the students measure the apparent depth of a penny (image depth) versus the actual depth of the penny (object depth). To obtain the index of refraction, the image depth must be on the x-axis and the object depth on the y-axis.

Students look into the top of a graduated cylinder to sight a penny at the bottom. They use their finger to estimate the apparent position of the penny. The distance from the surface of the water to the image of the penny is the apparent depth. The actual depth is also measured.

When a spreadsheet is used to analyze this data, two tables and two graphs are produced. With Desmos two tables can be plotted on one graph. The ability of Desmos to graph the data and perform a linear regression in the laboratory was used to provide a near real time look at the data.

The green dots are mirror data with the image data on the x-axis. While the object distance data is the independent variable, and the image distance data is the dependent variable for both experiments, the refraction data only produces the index of refraction for water when the apparent depth (image distance) data is on the x-axis.

A student predicted that the image distance would be less than the object distance for the mirror, and data taken by another group supported this theory.

Refraction data with the image depth on the x-axis, object depth on the y-axis.

The result is about 10% above the expected, published value for the index of refraction of water.

When asked in class whether they preferred working with a spreadsheet or Desmos for graphing and analysis, the students orally responded that they like Desmos. The added step of screen capture and pasting into their document does not seem to be an impediment to use of Desmos. The students seem to take quickly to the tilde notation and the xn, yn variable structure.

The dynamic interactivity of Desmos appears to help - as soon as they type y1~mx1, a line appears through their data. Thus the function precedes the line. In some spreadsheets, one can right click to add the trendline to a graph and then right click to add the equation. This means that the line appears ahead of the equation, making the genesis of the line more mysterious. In Desmos the equation clearly drives the line. And Desmos first generates a direct relationship, whereas in spreadsheets one has to "force the y-intercept" to zero - a capability not yet found in all spreadsheets. The upshot is that Desmos has an intuitive feel.

With data entered and saved in Desmos in the laboratory, one can then later access the data and graphs from a desktop. Desmos fundamentally changes the accessibility of data graphing in the science laboratory. The patterns underneath a system come to life for the students.

Vanessa, Moesha

Working as a team, a pair of students determines the apparent image location behind a mirror tile. This laboratory appears to have an odd twist. If the students expect that the distances are equal, they tend to wind up with measurements that support equal distances. The graph of the image distance versus the object distance has a slope of one.

Dorothy, Tedrick

If the students expect that the image distance is less than the object distance, then they appear to make measurements that support that expectation. In most terms the students predict equality of the distances and find support for that. Every few terms a student will first propose inequality prior to the laboratory and data will be found to support that inequality. Sample sizes are too small and data has not been tracked to prove that this occurs reliably.

Pellida

In the refraction portion of the laboratory the students measure the apparent depth of a penny (image depth) versus the actual depth of the penny (object depth). To obtain the index of refraction, the image depth must be on the x-axis and the object depth on the y-axis.

Kimsky.

Students look into the top of a graduated cylinder to sight a penny at the bottom. They use their finger to estimate the apparent position of the penny. The distance from the surface of the water to the image of the penny is the apparent depth. The actual depth is also measured.

When a spreadsheet is used to analyze this data, two tables and two graphs are produced. With Desmos two tables can be plotted on one graph. The ability of Desmos to graph the data and perform a linear regression in the laboratory was used to provide a near real time look at the data.

The green dots are mirror data with the image data on the x-axis. While the object distance data is the independent variable, and the image distance data is the dependent variable for both experiments, the refraction data only produces the index of refraction for water when the apparent depth (image distance) data is on the x-axis.

A student predicted that the image distance would be less than the object distance for the mirror, and data taken by another group supported this theory.

Refraction data with the image depth on the x-axis, object depth on the y-axis.

The result is about 10% above the expected, published value for the index of refraction of water.

When asked in class whether they preferred working with a spreadsheet or Desmos for graphing and analysis, the students orally responded that they like Desmos. The added step of screen capture and pasting into their document does not seem to be an impediment to use of Desmos. The students seem to take quickly to the tilde notation and the xn, yn variable structure.

The dynamic interactivity of Desmos appears to help - as soon as they type y1~mx1, a line appears through their data. Thus the function precedes the line. In some spreadsheets, one can right click to add the trendline to a graph and then right click to add the equation. This means that the line appears ahead of the equation, making the genesis of the line more mysterious. In Desmos the equation clearly drives the line. And Desmos first generates a direct relationship, whereas in spreadsheets one has to "force the y-intercept" to zero - a capability not yet found in all spreadsheets. The upshot is that Desmos has an intuitive feel.

With data entered and saved in Desmos in the laboratory, one can then later access the data and graphs from a desktop. Desmos fundamentally changes the accessibility of data graphing in the science laboratory. The patterns underneath a system come to life for the students.

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