An experiment to measure the refractive index of a substance was carried out by a student - Leaving Cert Physics - Question 3 - 2023

The student would have taken the following measurements during the experiment:

1. Angle of Incidence (i): This is the angle between the incident ray and the normal to the surface at the point of incidence.
2. Angle of Refraction (r): This is the angle between the refracted ray and the normal.
3. Real Depth: The actual depth of the liquid in the container.
4. Apparent Depth: Depth as perceived by the observer, which is affected by the refractive index.
5. Critical Angle: The minimum angle of incidence at which total internal reflection occurs.
6. Partial Answers: These might include angles or the heights measured. Measurements could also be inferred from the diagram presented.

The refractive index (n) of the substance can be calculated using Snell's Law, which states:

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

Where:

• i is the angle of incidence,
• r is the angle of refraction.

Additionally, using the real depth (d) and apparent depth (h):

$n = \frac{\text{real depth}}{\text{apparent depth}}$

By collecting several measurements of incidences and refractions alongside the respective depths, the student can analyze the relationship and derive the refractive index through these mathematical relationships.

The student repeated the experiment for several reasons:

• To Increase Accuracy: Multiple trials help in minimizing errors and provide more reliable results.
• To Gather More Data: A larger set of data allows for better statistical analysis and understanding of variances.
• To Ensure Consistency: Repeating the setup ensures that any anomalies can be identified and corrected, confirming the validity of the observed data.
• To Draw a Graph: A larger dataset aids in creating a more accurate graph, which can be useful for visual representation of the relationship between angles and refractive indices.