An experiment was carried out to measure the refractive index of a substance - Leaving Cert Physics - Question 3 - 2008

Several key measurements are taken to calculate the refractive index:

1. Angle of Incidence (i): The angle between the incident ray and the normal at the surface of the substance.
2. Angle of Refraction (r): The angle between the refracted ray and the normal within the substance.
3. Real Depth: The actual thickness of the substance measured using a ruler.
4. Apparent Depth: This is the depth as seen from above, typically measured with angles or using a protractor.
5. Critical Angle: This is the angle calculated when light refracts at 90 degrees to the normal.

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

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

Additionally, measurements can be incorporated where:

• Real depth (r) is obtained from physical measurement.
• Apparent depth can be inferred through visual measurements at the angles determined.

Hence the formula for calculating the refractive index can be expressed as: $n = \frac{r}{\text{apparent depth}}$ This provides a systematic approach to deriving the refractive index based on measured values.

The experiment was repeated for several reasons:

1. To Increase Accuracy: Repeating the experiment helps to minimize errors and acquire more reliable data.
2. To Reduce Errors: Variability can occur due to environmental factors or measurement inaccuracies, thus repetition helps in averaging out these errors.
3. To Confirm Results: By repeating the experiment, one can confirm the consistency of the results obtained.