A layer of liquid B floats on liquid A. A ray of light...

A layer of liquid $B$ floats on liquid $A$. A ray of light begins in liquid $A$ and undergoes total internal reflection at the interface between the liquids when the angle of incidence exceeds $36.5^{\circ} .$ When liquid $B$ is replaced with liquid $C$, total internal reflection occurs for angles of incidence greater than $47.0^{\circ}$. Find the ratio $n_{B} / n_{C}$ of the refractive indices of liquids $B$ and $C$.

Key Concepts

Snell's Law

Snell's Law describes the relationship between the angles of incidence and refraction when light passes between two media with different refractive indices. It states that n? sin ?? = n? sin ??, where n? and n? are the refractive indices of the respective media, and ?? and ?? are the corresponding angles measured from the normal to the interface.

Critical Angle

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the less dense medium becomes 90°. It is defined by the relationship sin(?c) = n?/n?, where n? is the refractive index of the denser medium and n? is that of the less dense medium. This concept is fundamental when analyzing conditions for total internal reflection.

Total Internal Reflection

Total internal reflection occurs when the angle of incidence exceeds the critical angle, causing light to be completely reflected back into the denser medium. This happens when light attempts to move from a medium with a higher refractive index to one with a lower refractive index, preventing any refraction into the second medium.

Refractive Index

The refractive index measures how much the speed of light is reduced inside a medium compared to its speed in vacuum. It is a crucial parameter in optics, determining how much light bends, or refracts, when entering a material. Variations in refractive indices between materials are at the core of many optical phenomena including refraction, reflection, and dispersion.

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