An experiment to measure the refractive index of a substance was carried out by a student - Leaving Cert Physics - Question 3 - 2013

The student took several measurements during the experiment:

1. Angle of Incidence (i): Measured using the protractor, this angle represents the angle between the incident ray and the normal line at the boundary of the medium.
2. Angle of Refraction (r): Also measured with the protractor, this angle is the angle between the refracted ray and the normal line.
3. Real Depth: The actual depth of the liquid in the glass/plastic block.
4. Apparent Depth: The perceived depth as observed from above, influenced by the light's refraction.
5. Critical Angle: This can also be determined based on the values of incidence and refraction.
6. Height: If necessary, the student may have also measured the height for further calculations.

The student used the measured angles to calculate the refractive index using Snell's law, which states:

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

Where:

• n is the refractive index,
• i is the angle of incidence,
• r is the angle of refraction.

The real depth and apparent depth measurements are also related as follows:

$\frac{\text{real depth}}{\text{apparent depth}} = \frac{\sin(r)}{\sin(i)}$

The final formula for calculating the refractive index is:

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

This allows the student to derive a clear equation to find the refractive index based on simple trigonometric relationships.

The student repeated the experiment to ensure accuracy and reliability in the results. Repetition helps to identify any inconsistencies or errors in measurements, allowing for an average to be taken, which improves the overall validity of the experiment. Additionally, repeating the experiment aids in confirming the observed values for drawing graphs or conducting further analysis.