(Modeling) Speed of Light When a light ray travels from one medium, such as air, to another medium, such as water or glass, the speed of the light changes, and the light ray is bent, or refracted, at the boundary between the two media. (This is why objects under water appear to be in a different position from where they really are.) It can be shown in physics that these changes are related by Snell's law c₁ = sin θ₁ , c₂ sin θ₂ where c₁ is the speed of light in the first medium, c₂ is the speed of light in the second medium, and θ₁ and θ₂ are the angles shown in the figure. In Exercises 81 and 82, assume that c₁ = 3 x 10⁸ m per sec. Find the speed of light in the second medium for each of the following. a. θ₁ = 46°, θ₂ = 31° b. θ₁ = 39°, θ₂ = 28°

Key Concepts

Refraction

Refraction is the bending of light as it passes from one medium to another due to a change in its speed. This phenomenon occurs at the interface between two different materials, such as air and water, causing the light to change direction. The degree of bending depends on the angle of incidence and the refractive indices of the two media.

Snell's Law

Snell's Law describes the relationship between the angles of incidence and refraction when light travels between two different media. Mathematically, it is expressed as c₁/sin(θ₁) = c₂/sin(θ₂), where c₁ and c₂ are the speeds of light in the first and second media, respectively. This law allows us to calculate the speed of light in a new medium based on the angles and the known speed in the original medium.

Speed of Light

The speed of light in a vacuum is approximately 3 x 10⁸ meters per second, denoted as c. When light travels through different media, its speed decreases depending on the medium's optical density. Understanding how to calculate the speed of light in various materials is crucial for solving problems related to refraction and optical phenomena.