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Chapter 32: Problem 18

You are under water in a pond and look up at the smooth surface of the water, noticing the sun in the sky. Is the sun in fact higher in the sky than it appears to you while under water, or is it lower?

Short Answer

Expert verified
Answer: The sun appears higher in the sky than its actual position to an observer underwater due to refraction.

Step by step solution

01

Understanding refraction

Refraction is the change in direction of a wave due to a change in its speed as it passes from one medium to another. In this case, when the sun is in the sky, its light travels through the air and then enters the water. The speed of light changes at the air-water boundary, causing the light to refract. This bending of light occurs due to the difference in the index of refraction of the two mediums (air and water).
02

Identifying Snell's Law

Snell's Law is used to determine the angle of refraction when light passes from one medium to another. It is derived from the relationship between the angles of incidence and refraction with the indices of refraction of the incident and transmitted media. Mathematically, Snell's Law is expressed as: n_1 \times \sin{\theta}_1 = n_2 \times \sin{\theta}_2 Here, n_1 and n_2 are the indices of refraction of the two media (air and water, respectively), while \theta_1 and \theta_2 are the angles of incidence and refraction, respectively.
03

Comparing the indices of refraction

In this scenario, the index of refraction for air (n_1) is approximately 1, while the index of refraction for water (n_2) is approximately 1.33. Since n_2 > n_1, when light passes from air to water, it bends towards the normal (a line perpendicular to the surface at the point of incidence).
04

Analyzing the apparent position of the sun

As the light enters the water and bends towards the normal, the angle \theta_2 becomes smaller than the angle \theta_1. This bending of light creates the illusion that the sun is at a higher position in the sky than its actual location. Therefore, to an observer underwater, the sun appears higher in the sky than it actually is.
05

Conclusion

Based on the analysis of refraction and the application of Snell's Law, it can be concluded that the sun appears higher in the sky than it actually is to an observer underwater.

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