In an experiment to measure the refractive index of a substance, a student used a rectangular block of the substance to measure the angle of incidence i and the corresponding angle of refraction r for a ray of light as it passed from air into the substance - Leaving Cert Physics - Question 2 - 2014

To determine the angle of refraction (r), the student used a rectangular block placed on a flat surface. The setup involves:

1. Incident Beam: The ray of light from a laser or light source is directed at the block.
2. Refraction Point: Mark the point where the ray enters the block.
3. Draw Normals: A normal line should be drawn perpendicular to the surface at the entry point.
4. Using a Protractor: The angle of incidence (i) is measured from the normal; the angle r is measured on the other side of the block to determine the refraction.

Ensure that all measurements are recorded accurately for consistency.

To calculate the refractive index (n), plot the sine of the angles:

1. Calculate $ext{sin}(i)$ and $ext{sin}(r)$ for all recorded angles:

   i (degrees)	r (degrees)	sin(i)	sin(r)
   20	13	0.34	0.23
   30	20	0.50	0.34
   40	27	0.64	0.39
   50	36	0.77	0.59
   60	40	0.87	0.64
   70	43	0.98	0.68

2. Plot sin(i) against sin(r) on a graph.

3. Fit a straight line to the points, ensuring that the slope is examined for consistency.

4. From the graph, determine the slope, which is approximated by n = rac{ ext{sin}(i)}{ ext{sin}(r)}. The calculated slope value can help find the refractive index.

1. Reduction of Error: By using a graph, the impact of random errors in individual angle measurements is minimized. It calculates the overall trend, providing a more accurate average instead of relying on individual data points.

2. Visual Representation: Graphing allows for a visual representation of the relationship between sin(i) and sin(r). This can reveal any outlier effects and ensure a more comprehensive analysis of the data collected.