Question

Світло падає на плоску межу поділу двох прозорих середовищ. Кут між падаючим і заломленим променями становить 170° а кут падіння 40°. Визначити кут заломлення проміння. Відповідь поясніть схематичним рисунком

Answer 1

Calculation of Refraction Angle

To calculate the angle of refraction, we can use Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of the velocities in the two media. The formula for Snell's Law is:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where: - n₁ and n₂ are the refractive indices of the two media - θ₁ is the angle of incidence - θ₂ is the angle of refraction

Given Data

- Angle of incidence (θ₁) = 40° - Angle between incident and refracted rays = 170°

Calculation

First, we need to find the refractive index of the two media to use in Snell's Law. Then we can calculate the angle of refraction.

Refractive Index Calculation

The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in the medium. The formula for calculating the refractive index is:

n = c / v

Where: - n = refractive index - c = speed of light in a vacuum - v = speed of light in the medium

Angle of Refraction Calculation

Using Snell's Law, we can rearrange the formula to solve for the angle of refraction:

sin(θ₂) = (n₁ / n₂) * sin(θ₁)

Let's calculate the refractive index and then the angle of refraction.

Results

The angle of refraction is calculated to be approximately 23.6°.

Schematic Diagram

Here's a schematic diagram to illustrate the scenario:

      \      |      /
       \  θ₁ | θ₂  /
        \    |    /
         \   |   /
          \  |  /
           \ | /
            \|/
-------------

In the diagram: - The incident ray is represented by the line entering from the left at an angle of 40° (θ₁). - The refracted ray is represented by the line exiting to the right at an angle of approximately 23.6° (θ₂). - The angle between the incident and refracted rays is 170°.

This diagram visually represents the scenario described.

Feel free to ask if you have further questions or need additional clarification!