Question

Сонячне світло падає на поверхню речовини, показник заломлення якої 1,45.Визначити кут падіння, якщо кут заломлення 27 градусів

Answer 1

Calculation of the Angle of Incidence

To determine the angle of incidence when the angle of refraction is 27 degrees and the refractive index is 1.45, we can use Snell's law. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media involved.

Mathematically, Snell's law can be expressed as:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

where: - n₁ is the refractive index of the initial medium (in this case, air) - θ₁ is the angle of incidence - n₂ is the refractive index of the second medium (in this case, the substance with a refractive index of 1.45) - θ₂ is the angle of refraction (given as 27 degrees)

To find the angle of incidence (θ₁), we rearrange the equation as follows:

θ₁ = arcsin((n₂ * sin(θ₂)) / n₁)

Substituting the given values, we have:

θ₁ = arcsin((1.45 * sin(27)) / 1)

Now, let's calculate the value of θ₁ using the given formula:

θ₁ ≈ arcsin(0.648) ≈ 40.4 degrees

Therefore, the angle of incidence is approximately 40.4 degrees.

Please note that the provided search snippets do not directly provide the calculation steps for this specific problem. However, the calculation is based on the well-known Snell's law, which is a fundamental principle in optics.