Experimental Determination of Refractive Index Using Light and Microwaves

Study of Reflection and Refraction of Electromagnetic Waves

Objectives

• Measure the refractive index of a prism for electromagnetic waves in the visible range (light) and for microwaves.
• Measure the angle of reflection of electromagnetic waves.
• Determine the critical angle when a ray of light passes from a medium of higher refractive index to one of lower refractive index, leading to total internal reflection.

Theoretical Background and Planning

Refraction occurs when a wave changes its propagation speed upon passing from one medium to another. This phenomenon changes the direction of the ray when it is incident obliquely to the interface between two media with different refractive indices.

This relationship is governed by Snell's Law:

n₁ sin θ_i = n₂ sin θ_t

Where n₁ and n₂ are the refractive indices of the first and second media, respectively, and θ_i and θ_t are the angles of incidence and refraction, respectively.

When light travels from a denser medium (n₁) to a less dense medium (n₂), the angle of refraction (θ_t) is greater than the angle of incidence (θ_i). In this scenario, if the angle of incidence (θ_i) exceeds the critical angle (θ_c), no refracted ray exists, and total internal reflection occurs.

Experimental Procedure

Part 1: Determining the Refractive Index of a Prism (Visible Light)

1. Place a prism on the graduated disc so that the light ray from the source is incident normally (at 0°) on the flat side of the prism.
2. Rotate the disc to change and measure the angle of incidence (θ_i).
3. Determine the angle of refraction (θ_t) using a ruler placed against the prism and the graduated disc edge.
4. Repeat the steps for two additional angles of incidence.
5. Calculate the refractive index (n₂) in each case using Snell's Law (assuming n₁ = 1 for air).

Measurements (Part 1)

Using Snell's Law (n₁ sin θ_i = n₂ sin θ_t):

• a) θ_i = 10°, θ_t = 7°. Calculated n₂ = 1.42
• b) θ_i = 30°, θ_t = 20°. Calculated n₂ = 1.46
• c) θ_i = 50°, θ_t = 30°. Calculated n₂ = 1.53

Observation: As the angle of incidence increases, the calculated refractive index tends to increase.

Part 3a: Refraction from Less Dense to More Dense Medium (n₁ < n₂)

Part 3b: Refraction from Denser to Less Dense Medium (n₁ > n₂)

Data Comparison (Part 3)

Note: In Part 3b (denser to less dense), the angle of refraction increases rapidly. Based on the conclusions, total internal reflection occurs when the angle of incidence is 50° or greater.

Part 4: Reflection and Refraction of Microwaves

This section details the measurement of the refractive index of a material (likely styrene) using microwaves.

Applying Snell's Law to determine the refractive index (n₁) of the material (assuming n₂ = 1 for air):

• Angle of Incidence (θ_i): 20°
• Angle of Refraction (θ_t): 28° (Derived from the measurement θ_i + θ_t = 20° + 8° = 28°)

n₁ = (1 · sin 28°) / sin 20°

The calculated refractive index for the material using microwaves was n₁ = 1.37.

Conclusions

In the development of this experiment, both reflected and refracted angles were successfully measured. Based on the data from Part 3b, it was determined that the critical angle lies between 40° and 50°, specifically measured at approximately 45°.

The experiment successfully demonstrated the application of Snell's Law to calculate the refractive index for both visible light (using a prism) and electromagnetic waves in the microwave range (using styrene).