Question

An expensive spotlight is located at the bottom of a gold-plated swimming pool of depth d = 2.10 m (see Figure). Determine the diameter of the circle from which light emerges from the tranquil surface of the pool.

Answer 1

The diameter of the circle from which light emerges is equal to the diameter of the spotlight at the bottom of the pool.

Step-by-step explanation:

To determine the diameter of the circle from which light emerges from the tranquil surface of the pool, we can use the concept of refraction. When light passes from a medium with a higher refractive index to a medium with a lower refractive index, it bends away from the normal. In this case, the light is traveling from the water into the air, so it bends away from the normal.

The angle of incidence is equal to the angle of reflection, and the angle of refraction can be calculated using Snell's law: n1*sin(theta1) = n2*sin(theta2). Since the angle of incidence is 0 degrees, sin(theta1) = 0 and theta1 = 0 degrees.

The refractive index of water is about 1.33 and the refractive index of air is about 1.00. Plugging these values into Snell's law, we get: 1.33*sin(0) = 1.00*sin(theta2). Solving for theta2, we find that theta2 = 0 degrees, which means the light travels parallel to the surface of the pool.

Since the light travels parallel to the surface of the pool, the diameter of the circle from which light emerges is equal to the diameter of the spotlight at the bottom of the pool.

Answer 2

The question touches upon determining a diameter of light emergence from a pool, calculating an opening diameter in a pool toy using fluid mechanics, and figuring out the depth needed to double atmospheric pressure in a lake. It involves optics and Bernoulli's equation in fluid mechanics.

Step-by-step explanation:

The question relates to the application of optics and fluid mechanics principles in physics, particularly concerning the behavior of light and Bernoulli's principle. When a spotlight, located at the bottom of a swimming pool with depth d = 2.10 m, shines upwards, the light that emerges will do so within a circular area. This circle's diameter can be estimated using principles such as the refraction of light at the interface between two media (in this case, water and air).

In the case of the pool toy described, the principles of fluid dynamics, specifically the continuity equation and Bernoulli's equation, can be employed to determine the unknown diameter of the opening from which water emerges. This is because the mass flow rate in a tube must be constant, so if the speed of water flow increases, the cross-sectional area must decrease. This allows for the calculation of the exit diameter based on the given velocities and initial diameter.

When discussing pressure in a fluid, such as water, the increase in pressure with depth relies on the density of the fluid and gravitational acceleration. The pressure increases by one atmosphere for every approximately 10 meters of depth, thus answering the multiple-choice question about depth and pressure.