(a) Light reflected at 62.5^∘ from a gemstone in a ring is completely polarized. Can the gem be

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(a) Light reflected at 62.5^∘ from a gemstone in a ring is...

(a) Light reflected at $62.5^{\circ}$ from a gemstone in a ring is completely polarized. Can the gem be a diamond? (b) At what angle would the light be completely polarized if the gem was in water?

Key Concepts

Brewster's Angle

Brewster’s angle is the specific angle of incidence at which light reflected from a surface is completely polarized. This occurs because, at Brewster’s angle, the reflected and refracted rays are perpendicular, causing the p-polarized light (parallel to the plane of incidence) to be eliminated in the reflection. The angle is determined by the relation tan(?B) = n2/n1, where n1 and n2 are the refractive indices of the initial and transmitting media, respectively.

Refractive Index

The refractive index of a material is a fundamental property that quantifies how much light slows down and bends when it passes through the medium. It plays a key role in determining the behavior of light at an interface, including the angle at which light is fully polarized upon reflection (Brewster’s angle). Variations in refractive index among different materials allow for their identification and characterization.

Effect of the Surrounding Medium

The medium surrounding an object directly influences the observed optical phenomena, such as polarization at Brewster’s angle. When an object is immersed in a medium other than air, the refractive index of that medium must be used in the Brewster’s angle formula, which alters the angle at which light is completely polarized. Understanding this effect is crucial when comparing measurements or verifying material properties in different environments.

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