In an experiment to verify Snell's law, a student measured the angle of incidence i and the angle of refraction r for a ray of light entering a substance - Leaving Cert Physics - Question 3 - 2005

1. Graph Setup: A graph is drawn with sin(i) on the x-axis and sin(r) on the y-axis.
2. Labelled Axes: Both axes are labelled appropriately with units.
3. Data Points: At least five data points are plotted based on the sin values calculated from the angle measurements.
4. Best Fit Line: A straight line is drawn to fit the plotted points, showing a linear relationship.
5. Conclusion: The relationship shows that sin(i) is proportional to sin(r), indicating that the ratio verifies Snell's law. A straight line through the origin demonstrates that the indices of refraction are constant.

1. Slope Calculation: The slope of the line is calculated using two points from the graph, say (x1, y1) and (x2, y2):

   $m = \frac{y_2 - y_1}{x_2 - x_1}$

2. Values Substitution: Substitute the coordinates of two points to find the slope. The student found the slope, m = 0.672.

3. Refractive Index Calculation: The refractive index (n) can be calculated as follows:

   $n = \frac{sin(i)}{sin(r)}$

4. Result: Assuming an average slope value yields n = 1.49.

Smaller angles of incidence produce larger angles of refraction, leading to more significant parallax errors when taking measurements. Additionally, near-zero angles can cause the light to bend less, making it harder to accurately measure the angles with the protractor.

Therefore, the precision of angle measurements decreases, contributing to a greater potential for error in calculating the refractive index.