A flashlight beam strikes the surface of a pane of glass (n = 1.56) at a 69° angle to the normal. What is the angle of refraction?

검증된 단계별 안내

Identify the given values: The angle of incidence (θ₁) is 69°, and the refractive index of the glass (n₂) is 1.56. The refractive index of air (n₁) is approximately 1.00.

Recall Snell's Law, which relates the angles of incidence and refraction to the refractive indices:

n

₁⁢sin⁢θ1=n₂⁢sin⁢θ2, where θ₁ is the angle of incidence, θ₂ is the angle of refraction, n₁ is the refractive index of the first medium, and n₂ is the refractive index of the second medium.

Rearrange Snell's Law to solve for the sine of the angle of refraction (sin(θ₂)):

\sin θ_{2} = n

₁⁢sin⁢θ1n₂.

Substitute the known values into the equation:

\sin θ_{2} = \frac{1.00 \sin 69 °}{1.56}

. Calculate the sine of 69° and divide by 1.56.

Finally, use the inverse sine function (arcsin) to find the angle of refraction (θ₂):

θ_{2} = \arcsin \frac{1.00 \sin 69 °}{1.56}

. This will give you the angle of refraction in degrees.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Snell's Law

Snell's Law describes the relationship between the angles of incidence and refraction when light passes between two different media. It is mathematically expressed as n1 * sin(θ1) = n2 * sin(θ2), where n represents the refractive indices of the media and θ represents the angles relative to the normal. This law is fundamental for calculating how light bends when entering a new medium.

Refractive Index

The refractive index (n) of a material quantifies how much light slows down as it travels through that material compared to its speed in a vacuum. A higher refractive index indicates that light travels more slowly in that medium. In this question, the glass has a refractive index of 1.56, which is essential 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 line at the surface of the medium, while the angle of refraction is the angle between the refracted ray and the normal. These angles are crucial for applying Snell's Law, as they determine how much the light will bend when transitioning from one medium to another.