Question

Луч подводного источника падает на поверхность воды под углом 25°. Под каким углом он выйдет в воздух?

Answer 1

Α=25  n1=1,33   n2=1    β- ?

n1*sinα=n2*sinβ
sinβ=1,33*sin25=0,56
β=34 градуса - ответ

Answer 2

Calculation of the Angle of Emergence

To determine the angle at which the light from an underwater source emerges into the air, we can use the principle of refraction. When light passes from one medium (water) to another medium (air), it changes direction due to the change in the speed of light.

The angle of incidence (θ1) is the angle at which the light enters the water, and the angle of emergence (θ2) is the angle at which the light leaves the water and enters the air.

According to Snell's Law, the ratio of the sines of the angles of incidence and emergence is equal to the ratio of the speeds of light in the two media:

sin(θ1) / sin(θ2) = v1 / v2

In this case, the angle of incidence (θ1) is given as 25°. We need to find the angle of emergence (θ2).

To solve for θ2, we need to know the refractive indices of water and air. The refractive index of water is approximately 1.33, and the refractive index of air is approximately 1.00.

Using the formula above, we can rearrange it to solve for θ2:

sin(θ2) = (v2 / v1) * sin(θ1)

Substituting the values, we get:

sin(θ2) = (1.00 / 1.33) * sin(25°)

Now we can calculate the value of sin(θ2) and then find the angle θ2 by taking the inverse sine (arcsine) of that value.

Let's calculate it:

sin(θ2) = (1.00 / 1.33) * sin(25°) = 0.751879699

Taking the inverse sine of 0.751879699, we find:

θ2 ≈ 48.4°

Therefore, the angle at which the light from the underwater source will emerge into the air is approximately 48.4°.

Please note that this calculation assumes a simplified model and does not take into account factors such as the shape of the water surface or the presence of other media between the water and air.