A vat in England nicknamed "Strongbow" is 19.7 m tall, but how wide is it? Suppose the vat is filled with water. A ray of light enters the water from the air at one end of the vat, reflects off the bottom at the vat's center, and exits at the opposite end of the vat. If the light's angle of incidence is 42.0 degrees, what is the vat's diameter?
-First, I used Snell's law to get the angle of refraction to be 30.1 degrees. However, I'm confused on how to construct my triangle? I made the long leg (y)= 19.7 m and I know it is a right triangle. Since I now have both the angles of refraction and incidence, where would they go in my triangle?
duplicate post; already answered
To construct your triangle in this scenario, you can use the following steps:
1. Start by drawing a horizontal line to represent the water-filled vat. This line represents the bottom of the vat where the ray of light reflects.
2. At one end of the line, draw a vertical line upwards to represent the height of the vat. Label this line as 'h' for height, which is given as 19.7 m in this case.
3. From the top of the vertical line, draw a diagonal line downwards towards the other end of the horizontal line. This diagonal line represents the path of the ray of light inside the vat.
4. At the end of the diagonal line, draw a vertical line downwards to meet the horizontal line. This line represents the depth at which the light ray exits the vat.
5. Now, you can see that the diagonal line, vertical line, and horizontal line form a right triangle. Label the horizontal line as 'x' and the vertical line as 'y'.
6. The angle of incidence (42.0 degrees) refers to the angle at which the light ray enters the water from the air. Place this angle at the top left vertex of the triangle.
7. The angle of refraction (30.1 degrees) refers to the angle at which the light ray bends or changes direction as it crosses the air-water interface. Place this angle a little below the horizontal line, making sure it is less than 90 degrees.
8. Now, in the triangle, you should have the following labels: 'h' for the vertical line (height), 'x' for the horizontal line (diameter), 'y' for the diagonal line (hypotenuse). Also, mark the angles of incidence and refraction as labeled previously.
By constructing this triangle, you can see how the given dimensions and angles relate to each other, and solve for the diameter 'x' of the vat using trigonometric functions like sine, cosine, or tangent.