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When a swimming pool is empty, the distance from the bottom of the pool to the ceiling is 24.1 m. The pool is now filled with chemical-filled water (index of refraction 1.7) to depth 5.6 m. How far above does the ceiling appear to be, in m, to a swimmer at the very bottom of the pool?

When a swimming pool is empty, the distance from the bottom of the pool to the ceiling is 24.1 m. The pool is now filled with chemical-filled water (index of refraction 1.7) to depth 5.6 m. How far above does the ceiling appear to be, in m, to a swimmer at the very bottom of the pool?

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### Refraction and Apparent Depth in a Swimming Pool **Problem Context:** When a swimming pool is empty, the distance from the bottom of the pool to the ceiling is 24.1 meters. The pool is then filled with chemical-filled water, which has an index of refraction of 1.7, up to a depth of 5.6 meters. **Question:** How far above does the ceiling appear to be, in meters, to a swimmer at the very bottom of the pool? **Concept Explanation:** This question involves the concept of refraction, where light changes direction when it passes from one medium to another—in this case, from water to air. The apparent depth can be calculated using the formula: \[ \text{Apparent Height} = \frac{\text{Actual Height in Water}}{\text{Index of Refraction}} + \text{Depth of Water}\] - **Index of Refraction (n):** A measure of how much the speed of light is reduced inside a medium. For the given problem, the index of refraction of the chemical-filled water is 1.7. **Solution Steps:** 1. Calculate the distance the ceiling appears to be above the swimmer by adjusting the true depth of 24.1 meters for the refraction. 2. Apply the formula to find the apparent height of the ceiling when viewed through 5.6 meters of water. Understanding this problem helps in comprehending how light behaves in different media and its effect on visual perception under water.
Transcribed Image Text:### Refraction and Apparent Depth in a Swimming Pool **Problem Context:** When a swimming pool is empty, the distance from the bottom of the pool to the ceiling is 24.1 meters. The pool is then filled with chemical-filled water, which has an index of refraction of 1.7, up to a depth of 5.6 meters. **Question:** How far above does the ceiling appear to be, in meters, to a swimmer at the very bottom of the pool? **Concept Explanation:** This question involves the concept of refraction, where light changes direction when it passes from one medium to another—in this case, from water to air. The apparent depth can be calculated using the formula: \[ \text{Apparent Height} = \frac{\text{Actual Height in Water}}{\text{Index of Refraction}} + \text{Depth of Water}\] - **Index of Refraction (n):** A measure of how much the speed of light is reduced inside a medium. For the given problem, the index of refraction of the chemical-filled water is 1.7. **Solution Steps:** 1. Calculate the distance the ceiling appears to be above the swimmer by adjusting the true depth of 24.1 meters for the refraction. 2. Apply the formula to find the apparent height of the ceiling when viewed through 5.6 meters of water. Understanding this problem helps in comprehending how light behaves in different media and its effect on visual perception under water.
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