Ch 34: Ray Optics

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 34: Ray Optics

문제 12

34장, 문제 12

A costume jewelry pendant made of cubic zirconia is submerged in oil. A light ray in the oil strikes one face of the zirconia crystal at an angle of incidence of 25°. Once inside, what is the ray's angle with respect to the face of the crystal?

검증된 단계별 안내

Identify the relevant physics concept: This problem involves the refraction of light, which is governed by Snell's Law. Snell's Law is expressed as:

n

₁⁢sin⁢θ₁=n₂⁢sin⁢θ₂, where

n

₁ and

n

₂ are the refractive indices of the two media, and

θ

₁ and

θ

₂ are the angles of incidence and refraction, respectively.

Determine the refractive indices: Look up the refractive index of oil (

n

₁) and cubic zirconia (

n

₂). For example, the refractive index of oil is approximately 1.46, and the refractive index of cubic zirconia is approximately 2.15.

Apply Snell's Law: Substitute the known values into Snell's Law. For this problem,

n

₁=1.46,

θ

₁=25°, and

n

₂=2.15. The equation becomes:

1.46 \sin 25 ° = 2.15 \sin θ

₂.

Solve for the angle of refraction: Rearrange the equation to isolate

\sin θ

₂:

\sin θ

₂=1.46⁢sin⁢25°2.15. Then, calculate

θ

₂ by taking the inverse sine of the result:

θ

₂=sin⁢−1⁢1.46⁢sin⁢25°2.15.

Interpret the result: The angle

θ

₂ is the angle of refraction inside the cubic zirconia. To find the ray's angle with respect to the face of the crystal, subtract

θ

₂ from 90°:

90 ° - θ

₂. This gives the desired angle.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Snell's Law

Snell's Law describes how light rays change direction when they pass from one medium to another. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and is equal to the ratio of the velocities of light in the two media. This principle is essential for determining the angle of the light ray as it enters the cubic zirconia from the oil.

Refractive Index

The refractive index is a dimensionless number that describes how fast light travels in a medium compared to its speed in a vacuum. Each material has a specific refractive index, which affects how much light bends when entering or exiting the material. For cubic zirconia and oil, knowing their refractive indices is crucial for applying Snell's Law to find the angle of refraction.

Angle of Incidence and Angle of Refraction

The angle of incidence is the angle between the incoming light ray and the normal (perpendicular) line to the surface at the point of incidence. The angle of refraction is the angle between the refracted ray and the normal. Understanding these angles is vital for calculating how the light ray behaves as it transitions from oil into the cubic zirconia crystal.