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?
Let vat radius = r
To leave at the opposite edge, the beam must strike the middle of the vat bottom.
tan 30.1 = r/h = 0.5796
r = 11.42 m
Thank you!
To construct the triangle, you can visualize the ray of light entering the water at one end of the vat and exiting at the opposite end after reflecting off the bottom at the vat's center. Here's how you can set up the triangle:
1. Draw a horizontal line to represent the water surface at the top of the vat.
2. Draw a vertical line downwards from the left end of the water surface to represent the ray of light entering the water.
3. Draw another vertical line upwards from the right end of the water surface to represent the ray of light exiting the water.
4. Connect the bottom ends of the two vertical lines with a diagonal line to represent the path of the ray of light as it reflects off the vat's bottom.
Now, assign the following labels to the triangle:
- The horizontal line between the two vertical lines represents the water surface and is the base of the triangle.
- The vertical line to the left represents the incoming ray of light and is the incident ray.
- The vertical line to the right represents the outgoing ray of light and is the refracted ray.
- The diagonal line represents the path of the reflected ray and is perpendicular to the water surface.
Now, let's label the angles on the triangle:
- The angle of incidence (42.0 degrees) should be labeled as the angle between the incident ray and the water surface.
- The angle of refraction (30.1 degrees) should be labeled as the angle between the refracted ray and the water surface.
Now, your triangle is set up with the angles labeled correctly. The length of the vertical line representing the vat's height (y) is correctly assigned as 19.7 m. With this setup, you can proceed to solve for the diameter of the vat.