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?

Question

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?

drwls · Answer

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

Ashley · Answer

Thank you!