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 find the angle of refraction, the student used a rectangular block of the substance and measured the angles using a protractor.

1. Set up the experiment: The rectangular block is placed on a flat surface, and a ray of light is directed at it from the air at an angle of incidence, i.
2. Mark the incident ray: The path of the incident ray is drawn until it hits the surface of the block.
3. Indicate normal and refracted rays: A normal line is drawn at the point of incidence perpendicular to the surface of the block. The angle of refraction, r, is measured from the normal to the path of the refracted ray inside the block.
4. Use a protractor: The angle of refraction is measured using a protractor, ensuring to properly align the edges for accuracy.

Diagram: Include a diagram showing the incident ray, normal line, and the refracted ray, with angles labelled.

To calculate the refractive index, draw a graph of sin(i) against sin(r).

1. Calculate sin(i) and sin(r) for each pair of angles:

   i (degrees)	r (degrees)	sin(i)	sin(r)
   20	13	0.34	0.22
   30	27	0.50	0.45
   40	23	0.64	0.39
   50	36	0.77	0.59
   60	40	0.87	0.64
   70	43	0.94	0.69

2. Plot the points on a graph with sin(i) on the x-axis and sin(r) on the y-axis.

3. Draw a line of best fit through the points.

4. Determine the slope of the line. The refractive index (n) is calculated using the formula: $n = \frac{ \sin(i) }{ \sin(r) }$ For values close to the line, calculating the slope will yield a refractive index of approximately 1.44 based on the linear relationship observed.

1. Minimization of errors: When using a graph, the slope calculated accounts for all the pairs of angles simultaneously, effectively minimizing random errors that may occur with single measurements. This leads to a more consistent and reliable value for the refractive index.
2. Identification of outliers: A graphical method allows for the visual identification of outliers or inconsistencies in the data. It becomes easier to spot any points that do not fit the expected trend, ensuring that the final value calculated is based on the most accurate data.