Question

Столб вбит в дно реки и возвышается над водой на 1 м. Найти длину тени столба на дне реки , если высота Солнца над горизонтом равна 30, глубина реки 2 м , а показатель преломления воды равен 1,33.

Answer 1

Ответ:

1,4 м

Объяснение:

Дано:

H₁ = 1 м

α = 30°

H₂ = 2 м

n = 1,33

_________

x - ?

1)

Сделаем чертеж.

2)

tg α = BC / AB = BC / H₁

BC = H₁·tgα = 1·tg 30° = 1·√3 / 3 ≈ 0,58 м

3)

sin α / sin β = n

sin β = sin α / n = sin 30° / n = 0,5 / 1,33 ≈ 0,376

β ≈ 22°

4)

tg β = EF  / CE = EF / H₂

EF = H₂·tg β = 2·tg 22° = 2·0,404 ≈ 0,81 м

5)

x = DE+EF = BC + EF = 0,58 + 0,81 ≈ 1,4 м

Answer 2

Calculation of the Shadow Length

To find the length of the shadow cast by the column at the bottom of the river, we can use the principles of geometric optics and Snell's law. Snell's law relates the angles of incidence and refraction when light passes through different media.

Given: - Height of the column above the water surface: 1 m - Height of the Sun above the horizon: 30° - Depth of the river: 2 m - Refractive index of water: 1.33

To calculate the length of the shadow, we need to determine the angle of incidence and the angle of refraction.

Calculation Steps:

1. Calculate the angle of incidence: - The angle of incidence is the angle between the Sun's rays and the horizontal plane. - Since the height of the Sun above the horizon is given as 30°, the angle of incidence can be calculated as 90° - 30° = 60°.

2. Calculate the angle of refraction: - The angle of refraction is the angle between the refracted rays and the horizontal plane. - To calculate the angle of refraction, we need to use Snell's law: n1 * sin(theta1) = n2 * sin(theta2), where n1 and n2 are the refractive indices of the initial and final media, and theta1 and theta2 are the angles of incidence and refraction, respectively. - In this case, the initial medium is air (refractive index = 1) and the final medium is water (refractive index = 1.33). - Plugging in the values, we have: 1 * sin(60°) = 1.33 * sin(theta2). - Solving for theta2, we find: theta2 = arcsin(sin(60°) / 1.33) ≈ 43.49°.

3. Calculate the length of the shadow: - The length of the shadow can be calculated using the tangent function: shadow length = depth of the river * tan(theta2). - Plugging in the values, we have: shadow length = 2 * tan(43.49°) ≈ 1.81 m.

Therefore, the length of the shadow cast by the column at the bottom of the river is approximately 1.81 meters.