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 34

34장, 문제 34

A laser beam in air is incident on a liquid at an angle of 53° with respect to the normal. The laser beam's angle in the liquid is 35°. What is the liquid's index of refraction?

검증된 단계별 안내

Identify the relevant physics principle: This problem involves Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of two media. The formula is:

n

₁⁢sin⁢θ₁=n₂⁢sin⁢θ₂, where

n

₁ and

n

₂ are the indices of refraction of the first and second medium, and

θ

₁ and

θ

₂ are the angles of incidence and refraction, respectively.

Assign known values: The index of refraction of air is approximately

n

₁=1.00. The angle of incidence is

θ

₁=53°, and the angle of refraction in the liquid is

θ

₂=35°. The goal is to find the liquid's index of refraction,

n

₂.

Rearrange Snell's Law to solve for the unknown index of refraction:

n

₂=n₁⁢sin⁢θ₁sin⁢θ₂.

Substitute the known values into the equation:

n

₂=1.00⁢sin⁢53°sin⁢35°.

Use a scientific calculator to compute the sine values for the angles and divide them to find

n

₂. Ensure your calculator is in degree mode when calculating the sine of the angles.

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주요 개념

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Snell's Law

Snell's Law describes the relationship between the angles of incidence and refraction when a wave passes between two different media. It is mathematically expressed as n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the indices of refraction of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively. This law is fundamental in understanding how light behaves at the interface of different materials.

Index of Refraction

The index of refraction (n) is a dimensionless number that describes how fast light travels in a medium compared to its speed in a vacuum. It is defined as n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium. A higher index indicates that light travels slower in that medium, which affects how light bends when entering or exiting the material.

Angle of Incidence and Refraction

The angle of incidence is the angle between the incident ray and the normal line at the point of contact on the surface, while the angle of refraction is the angle between the refracted ray and the normal. These angles are crucial for applying Snell's Law to determine how light changes direction when transitioning between different media, such as air and liquid in this scenario.