A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. She looks at a penny that is on the bottom of the pool directly below her. To her, the penny appears to be a distance of 7.00 m from her. What is the depth of the water at this point?

검증된 단계별 안내

Understand the problem: The apparent depth of the penny is given as 7.00 m, and the person is 3.00 m above the water surface. The goal is to find the actual depth of the water using the concept of refraction and the refractive index of water.

Recall the formula for apparent depth: The relationship between the apparent depth \(d_a\) and the real depth \(d_r\) is given by \(d_a = \frac{d_r}{n}\), where \(n\) is the refractive index of water (approximately 1.33 for visible light).

Rearrange the formula to solve for the real depth \(d_r\): \(d_r = d_a \cdot n\). Substitute \(d_a = 7.00 \ \text{m}\) and \(n = 1.33\) into the equation.

Account for the height of the person above the water: The total depth of the water is the real depth \(d_r\) minus the height of the person above the water surface (3.00 m).

Combine the results: Add the height of the person above the water to the calculated real depth \(d_r\) to determine the total depth of the water at the point where the penny is located.

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주요 개념

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

Refraction of Light

Refraction is the bending of light as it passes from one medium to another, such as from air to water. This bending occurs because light travels at different speeds in different materials. In this scenario, the apparent depth of the penny is affected by the refraction of light, making it appear deeper than its actual position.

Apparent Depth

Apparent depth refers to the perceived distance of an object submerged in a fluid, which differs from its actual depth due to refraction. When viewing an object underwater from above, the light rays bend, causing the object to appear closer to the surface than it truly is. This concept is crucial for understanding the discrepancy between the actual depth of the penny and how deep it appears to the observer.

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. This law helps calculate the apparent depth and is essential for solving the problem of determining the actual depth of the water based on the observed distance.