A horizontal, parallel-sided plate of glass having a refractive index of 1.52 is in contact with the surface of water in a tank. A ray coming from above in air makes an angle of incidence of 35.0° with the normal to the top surface of the glass. What angle does the ray refracted into the water make with the normal to the surface?

검증된 단계별 안내

Identify the mediums involved: air, glass, and water. The refractive indices are n_air = 1.00, n_glass = 1.52, and n_water = 1.33.

Apply Snell's Law at the air-glass interface. Snell's Law is given by:

n_{1} \sin θ = n_{2} \sin θ

. Here, n1 = 1.00 (air), θ1 = 35.0°, and n2 = 1.52 (glass). Solve for the angle of refraction θ2 in the glass.

Calculate the angle of refraction in the glass using the formula:

\sin θ = \frac{n_{1} \sin θ}{n_{2}}

. Substitute the known values to find θ2.

Apply Snell's Law again at the glass-water interface. Use n_glass = 1.52 and n_water = 1.33. The angle of incidence at this interface is the angle of refraction from the previous step.

Solve for the angle of refraction in the water using Snell's Law:

n_{2} \sin θ = n_{3} \sin θ

. Substitute the values to find the angle of refraction in the water.

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주요 개념

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

Snell's Law

Snell's Law describes how light bends when it passes from one medium to another. It is given by the equation n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively. This law is crucial for calculating the angle of refraction when light enters a different medium.

Refractive Index

The refractive index of a medium quantifies how much light slows down and bends when entering the medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. A higher refractive index indicates greater bending of light. In this problem, the refractive indices of air, glass, and water are essential for applying Snell's Law.

Angle of Incidence and Refraction

The angle of incidence is the angle between the incoming ray and the normal to the surface at the point of entry. The angle of refraction is the angle between the refracted ray and the normal. Understanding these angles is crucial for applying Snell's Law to determine how the ray bends as it passes through different media, such as from air to glass and then to water.