Introduction

Relevance of the Topic

The study of Geometric Optics: Refractive Index is a crucial part of the High School Physics curriculum, as it is a foundation for understanding everyday phenomena such as rainbows, mirages, how glasses correct vision imperfections, and cutting-edge technologies like fiber optics and lasers. This is a gateway to understanding how light interacts with different media and is essential for the development of notions of applied Physics.

Contextualization

Framed within the Optics unit, the study of the refractive index is closely related to other topics such as reflection, refraction, and light dispersion. A deep understanding allows calibrating the view on refraction and reflection phenomena, contributing to the decoding of universal laws of light behavior. In addition, calculating the refractive index is fundamental for the quantitative analysis of these phenomena and brings to light the mathematical nature of Physics, demonstrating how this discipline is indeed an exact science.

Theoretical Development

Components:

• The Phenomenon of Refraction: Refraction occurs when a light ray passes from one medium to another, altering its direction. Refraction is possible due to the difference in refractive indices between the two media, which causes a change in the speed of light and, consequently, in its direction.

• Speed of Light in Different Media: The speed of light varies according to the medium in which it propagates. In a vacuum, light has the highest possible speed, approximately 300,000 km/s. In other media, light travels at a slower speed, depending on the refractive index of the medium.

• Snell's Law: This law determines the behavior of light as it passes from one medium to another. The law establishes that the product of the sine of the angle of incidence by the speed of light in the first medium is equal to the product of the sine of the angle of refraction by the speed of light in the second medium.

• Angle of Incidence and Angle of Refraction: The angle of incidence is the angle between the incident ray and the normal line at the point of incidence. The angle of refraction is the angle between the refracted ray and the normal line. Both angles are measured from the normal, a line perpendicular to the surface at the point of incidence.

• Absolute Refractive Index: The absolute refractive index (n) of a medium is given by the ratio between the speed of light in a vacuum (c) and the speed of light in the medium (v), n = c/v. This index indicates how much light slows down when entering a medium.

• Relative Refractive Index: The relative refractive index between two media is the ratio between their absolute refractive indices. It describes how much light changes speed when passing from one medium to another.

Key Terms:

• Refraction: It is the phenomenon that occurs when a light ray changes direction when passing from one medium to another.

• Refractive Index: It is a measure of the change in the speed of light when passing from one medium to another.

• Snell's Law: It is a formula used to calculate the angle of refraction or the refractive index when some parameters are known.

• Angle of Incidence and Refraction: Angles formed by the light ray and the normal, with the incidence angle related to the ray incident on the surface and the refraction angle to the refracted ray.

Examples and Cases:

• Calculation of Absolute Refractive Index: If the speed of light in a certain medium is 200,000 km/s, the absolute refractive index in that medium would be n = c/v = 300,000/200,000 = 1.5. This means that light travels 1.5 times slower in that medium than in a vacuum.

• Application of Snell's Law: If a light ray strikes a glass surface (refractive index 1.5) at an angle of 30° coming from air (refractive index 1.0), the angle of refraction can be calculated using Snell's Law. The result is an angle of refraction of approximately 19.5°.

• Calculation of Relative Refractive Index: If we have two media, the first with a refractive index of 1.0 (air) and the second with a refractive index of 1.5 (glass), the relative refractive index of glass compared to air would be 1.5/1.0 = 1.5. This means that light travels 1.5 times slower in glass than in air.

Detailed Summary

Key Points:

• Refraction: Understanding the phenomenon of refraction unveils the transformations of light rays when interacting with different media. It is essential to realize that a change of medium alters the speed and direction of light, giving rise to the phenomenon of refraction.

• Snell's Law: Essential for quantifying refraction. It connects the angle of incidence, the angle of refraction, and the refractive indices of the involved media. It is a fundamental tool for calculating the angular deviation of light.

• Absolute and Relative Refractive Indices: Key concepts for calculating the speed of light in different media. The absolute refractive index serves to understand how a specific medium influences the speed of light. On the other hand, the relative refractive index, when comparing two media, offers insights into the relative change in the speed of light.

Conclusions:

• Proximity to Everyday Phenomena: The study of Geometric Optics, especially the refractive index, allows understanding a variety of everyday phenomena and technologies, from the formation of rainbows to the functioning of corrective lenses and fiber optics.

• Exact Nature of Physics: The quantitative analysis of light refraction through refractive indices and Snell's Law reinforces Physics as an exact science, using Mathematics to explain and predict natural phenomena.

Exercises:

1. Calculation of Absolute Refractive Index: The speed of light in a substance is 225,000 km/s. Calculate the absolute refractive index of this substance.

2. Application of Snell's Law: A light ray passes from air (n=1.00) to an unknown medium, striking the separating surface at an angle of 45° and refracting at an angle of 30°. Determine the refractive index of the unknown medium.

3. Calculation of Relative Refractive Index: Knowing that the refractive index of glass is 1.5 and that of water is 1.33, calculate the relative refractive index of glass compared to water.