A scientist wants to demonstrate that dispersion depends on wavelength. She shines monochromatic red light through a prism. What does she observe and why?

The correct option is: Only a single red ray emerges; no spectrum forms because there is only one wavelength.

To understand why this is the case, let us break down the physical concepts of light, dispersion, and monochromatic sources step-by-step:

1. What is dispersion?
Dispersion is the phenomenon where a wave's phase velocity depends on its frequency or wavelength. When composite light (like white light, which contains a broad spectrum of wavelengths) passes through a dispersive medium like a glass prism, different wavelengths experience different refractive indices. The refractive index $n$ of glass is higher for shorter wavelengths (like violet) and lower for longer wavelengths (like red). As a result, different colors bend by different angles, spreading out to form a colorful spectrum.

2. What is monochromatic light?
The term "monochromatic" comes from the Greek words mono (single) and chroma (color). In physics, monochromatic light refers to light that consists of a single, precise wavelength (or a extremely narrow band of wavelengths). In this scenario, the scientist is using monochromatic red light, meaning there is only one wavelength of light entering the prism.

3. Why does no spectrum form?
Because the incoming light has only one wavelength, every portion of the beam experiences the exact same refractive index inside the prism. Consequently, all of the light bends (refracts) by the exact same angle. Since there are no other wavelengths present to bend at different angles, the light cannot be separated into different colors. Thus, the light simply emerges as a single refracted ray of red light, and no spectrum is formed.