We wish to determine the depth of a swimming pool filled...

We wish to determine the depth of a swimming pool filled with water by measuring the width $(x=5.50 \mathrm{m})$ and then noting that the bottom edge of the pool is just visible at an angle of $13.0^{\circ}$ above the horizontal as shown in Fig. $62 .$ Calculate the depth of the pool.

Key Concepts

Trigonometric Relationships in Optics

Trigonometric functions, particularly the tangent function, are used in optical problems to relate angles to physical distances such as depth and horizontal spans. In the given context, these relationships help to connect the measured horizontal distance to the depth of the pool by using the angle at which the bottom edge is observed, ultimately allowing for the calculation of the unknown depth.

Snell's Law

Snell's Law describes how light bends when it passes between two media with different refractive indices. It states that the product of the refractive index and the sine of the angle of incidence in the first medium equals that in the second medium. This law is the basis for understanding how and why light changes direction at the boundary, which is essential to problems involving refraction.

Critical Angle

The critical angle is the minimum angle of incidence within a denser medium above which all the light is totally internally reflected and none refracts into the less dense medium. It can be derived from Snell's Law by setting the refracted angle to 90 degrees. This concept is crucial in determining the condition under which the bottom of a pool becomes just visible at the water’s surface.

Total Internal Reflection

Total internal reflection is the phenomenon where light, traveling in a denser medium, is completely reflected back into that medium when the angle of incidence exceeds the critical angle. It is a direct consequence of the relationship defined by Snell's Law and is central to understanding optical behaviors in systems such as water-air interfaces.

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