Ch. 34 - The Wave Nature of Light: Interference and Polarization

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 34 - The Wave Nature of Light: Interference and Polarization

문제 54

33장, 문제 54

What would Brewster’s angle be for reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from above the surface.

검증된 단계별 안내

Determine Brewster's angle using the formula:

tan(θ

_B) = n₂ / n₁, where

n

₁ is the refractive index of the medium the light is coming from (water in this case) and

n

₂ is the refractive index of the medium the light is entering (air).

Rearrange the formula to solve for Brewster's angle:

θ

_B = arctan(n₂ / n₁). Substitute the refractive indices of water (

n

₁ ≈ 1.33) and air (

n

₂ ≈ 1.00).

Compare this Brewster's angle to the critical angle for total internal reflection. Use the formula for the critical angle:

θ

_c = arcsin(n₂ / n₁). Substitute the same refractive indices to calculate the critical angle.

Now, consider Brewster's angle for light coming from above the surface (air to water). Use the same formula for Brewster's angle:

θ

_B = arctan(n₂ / n₁), but this time

n

₁ = 1.00 (air) and

n

₂ = 1.33 (water).

Compare the Brewster's angles for light coming from beneath the surface and from above the surface, as well as the critical angle for total internal reflection. Discuss how these angles relate to the behavior of light at the water-air interface.

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주요 개념

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Brewster's Angle

Brewster's angle is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. It can be calculated using the formula θ_B = arctan(n2/n1), where n1 and n2 are the refractive indices of the two media. At this angle, the reflected and refracted rays are perpendicular to each other.

Total Internal Reflection

Total internal reflection occurs when a light wave traveling in a denser medium hits a boundary with a less dense medium at an angle greater than the critical angle. Instead of refracting, the light is completely reflected back into the denser medium. This phenomenon is crucial in fiber optics and occurs only when the light is moving from a medium with a higher refractive index to one with a lower refractive index.

Refractive Index

The refractive index is a dimensionless number that describes how light propagates through a medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. The refractive index affects how much light bends when entering or exiting a medium, influencing both Brewster's angle and the conditions for total internal reflection.