You shine a laser on a plastic prism made from an unknown material and measure the angles relative to the normal that the light takes both inside and outside the medium. You make a plot of sin Oinside versus sin Ooutside for the plastic object and calculate the slope of best-fit line of your plot to be 0.80000 + 0.0128. What is the index of refraction of the plastic object? (

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**Experimental Investigation: Determining the Index of Refraction**

**Objective:**
Determine the index of refraction for a plastic prism using light angles.

**Procedure:**
1. Shine a laser on a plastic prism made of an unknown material.
2. Measure the angles relative to the normal for the light's path both inside and outside the medium.
3. Plot the sine of the angle inside (\(\sin \theta_{\text{inside}}\)) versus the sine of the angle outside (\(\sin \theta_{\text{outside}}\)) for the plastic object.

**Data Analysis:**
- Calculate the slope of the best-fit line for your plotted data.

**Results:**
- The calculated slope is \(0.80000 \pm 0.0128\).

**Question:**
- What is the index of refraction of the plastic object?

**Explanation:**
In this experiment, the slope of the plot \((\sin \theta_{\text{inside}}\) vs \(\sin \theta_{\text{outside}})\) gives the index of refraction of the plastic, according to Snell's Law. The slope reflects the ratio of the speed of light in different media, which is a direct measure of the index of refraction. 

**Conclusion:**
The index of refraction of the plastic object is estimated to be \(0.80000\) with an uncertainty of \(0.0128\). This value provides insight into the optical properties of the material.
Transcribed Image Text:**Experimental Investigation: Determining the Index of Refraction** **Objective:** Determine the index of refraction for a plastic prism using light angles. **Procedure:** 1. Shine a laser on a plastic prism made of an unknown material. 2. Measure the angles relative to the normal for the light's path both inside and outside the medium. 3. Plot the sine of the angle inside (\(\sin \theta_{\text{inside}}\)) versus the sine of the angle outside (\(\sin \theta_{\text{outside}}\)) for the plastic object. **Data Analysis:** - Calculate the slope of the best-fit line for your plotted data. **Results:** - The calculated slope is \(0.80000 \pm 0.0128\). **Question:** - What is the index of refraction of the plastic object? **Explanation:** In this experiment, the slope of the plot \((\sin \theta_{\text{inside}}\) vs \(\sin \theta_{\text{outside}})\) gives the index of refraction of the plastic, according to Snell's Law. The slope reflects the ratio of the speed of light in different media, which is a direct measure of the index of refraction. **Conclusion:** The index of refraction of the plastic object is estimated to be \(0.80000\) with an uncertainty of \(0.0128\). This value provides insight into the optical properties of the material.
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