A light ray in air strikes the right-angle prism shown in...

A light ray in air strikes the right-angle prism shown in Fig. 33.46. This ray consists of two different wavelengths. When it emerges at face $A B,$ it has been split into two different rays that diverge from each other by $8.50^{\circ}$ . Find the index of refraction of the prism for each of the two wavelengths.

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Key Concepts

Dispersion

Dispersion is the phenomenon whereby the refractive index of a material varies with the wavelength of light. This wavelength dependency causes different colors (or wavelengths) of light to deviate by different amounts when passing through a prism, leading to the splitting of a ray into its constituent spectral components. Understanding dispersion is crucial for analyzing problems involving multi-wavelength light behavior.

Prism Geometry and Angular Deviation

The geometry of a prism, including its apex angle, determines how much a light ray is deviated as it passes through. When a ray enters a prism, it experiences refraction at both interfaces, and the resultant angular deviation is a function of both the prism’s shape and the refractive index of its material. This concept is essential for linking the observed deviation angles with the underlying material properties.

Snell's Law

Snell's Law is a fundamental principle that governs the refraction of light as it passes between media with different refractive indices. It relates the angles of incidence and refraction to the indices of refraction of the two media, forming the basis for analyzing how light rays bend at interfaces, such as when entering and exiting a prism.

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