Question

Стоящий у края бассейна человек видит дно у противоложной стенки бассейна в направлении под углом B=80 градусов к вертикали. Какой кажется ему глубина бассейна h и чему равна действительная глубина бассейна H, если глаз наблюдателя находится на высоте a=1,65м от уровня воды в бассейне, а длина бассейна j=12м? Показатель преломления на границе воздух-вода 1,33.

Answer 1

Problem Analysis

A person standing at the edge of a pool sees the bottom of the pool at an angle of 80 degrees to the vertical. The person's eye is at a height of 1.65m above the water level in the pool, and the length of the pool is 12m. The refractive index at the air-water interface is 1.33. We need to find the apparent depth of the pool (h) and the actual depth of the pool (H).

Apparent Depth (h)

The apparent depth (h) is the depth that the person perceives the pool to be. It is the distance from the observer's eye to the point where the light rays appear to come from after refraction at the air-water interface.

To find the apparent depth (h), we can use the formula:

h = a * tan(B)

where: - h is the apparent depth - a is the height of the observer's eye above the water level - B is the angle between the line of sight and the vertical

Substituting the given values: - a = 1.65m - B = 80 degrees

We can calculate the apparent depth (h) using the formula.

Actual Depth (H)

The actual depth (H) is the true depth of the pool. It is the distance from the observer's eye to the bottom of the pool.

To find the actual depth (H), we can use the formula:

H = h / n

where: - H is the actual depth - h is the apparent depth - n is the refractive index of water with respect to air

Substituting the given values: - h (calculated in the previous step) - n = 1.33

We can calculate the actual depth (H) using the formula.

Calculation

Let's calculate the values of h and H using the given information.

Solution

Using the given values: - a = 1.65m - B = 80 degrees - j = 12m - n = 1.33

We can calculate the apparent depth (h) using the formula: h = a * tan(B)

Substituting the values: h = 1.65m * tan(80 degrees)

Calculating the value of h: h ≈ 5.77m

Now, we can calculate the actual depth (H) using the formula: H = h / n

Substituting the values: H = 5.77m / 1.33

Calculating the value of H: H ≈ 4.34m

Therefore, the person perceives the depth of the pool to be approximately 5.77m (h), but the actual depth of the pool is approximately 4.34m (H).

Please note that the calculations are approximate and may vary slightly depending on the exact values used.