A ray of light will undergo total internal reflection when it travels from a denser medium to a less dense medium and strikes the boundary at an angle greater than the critical angle. To determine which color should replace the blue ray to achieve total internal reflection, we need to understand the relationship between the refractive index and color.
Refractive Index and Color
The refractive index of a medium is a measure of how much light bends when it passes through the medium. Different colors of light have different wavelengths, and therefore, different refractive indices. For example, blue light has a shorter wavelength than red light, and its refractive index is higher in most materials.
Total Internal Reflection
Total internal reflection occurs when the angle of incidence is greater than the critical angle. The critical angle is the angle at which the refracted ray travels along the boundary between the two media. The critical angle depends on the refractive indices of the two media.
Determining the Replacement Color
Since the question does not specify the media involved, we can assume the blue ray is traveling from a denser medium to a less dense medium. To achieve total internal reflection, we need to replace the blue ray with a color that has a lower refractive index. Since red light has a longer wavelength and a lower refractive index than blue light, red light would be the best replacement.
Practical Insight
In optical fibers, which rely on total internal reflection to transmit light, the core is typically made of a material with a higher refractive index than the cladding. This ensures that light entering the core will be reflected back into the core, allowing for efficient transmission over long distances.
