How to Calculate the Observer's Viewing Angle in a Refraction Problem?

[U571-Phys]

A cylindrical opaque drinking glass has a diameter of 4.7 cm and a hieght h. An observer's eye is placed to where they are just barely looking over the rim of the glass. When the glass is empty, the observer can just barely see the edge of the bottom of the glass. When the glass is filled to be brim, the observer can just barely see the center of the bottom of the glass. The liquid in teh glass has an index of refraction of 1.29. Calculate the angle at which the observer is looking into the glass.

I could use Snell's law if I could figure out one of the angles in the equation. I am not sure on how to start this problem. Does anyone have an idea on how to obtain one of the angles from the information given. I know it has to be something simple that I am not thinking of.

 

[U571-Phys]

never mind
found a way

thanks anyways guys!

-U

 

[kyle8921]

Hello,

Thank you for sharing your problem. It seems like you are on the right track by considering Snell's law. However, in order to use this law, we need to know the angle of incidence (the angle at which light enters the glass) and the angle of refraction (the angle at which light bends as it travels through the glass).

To find the angle of incidence, we can use the fact that the observer's eye is just barely looking over the rim of the glass. This means that the observer's line of sight is parallel to the top of the glass. We can draw a right triangle with the height of the glass (h) as the opposite side and the observer's line of sight as the adjacent side. The angle between these two sides is the angle of incidence.

Now, to find the angle of refraction, we can use the fact that the observer can just barely see the edge of the bottom of the glass when it is empty, and the center of the bottom of the glass when it is filled. This means that the light is bending at the interface between the air and the glass, and then again at the interface between the glass and the liquid. We can use Snell's law twice to find the angle of refraction.

Once we have both angles, we can use Snell's law (n1sinθ1 = n2sinθ2) to solve for the angle at which the observer is looking into the glass.

I hope this helps. Good luck with your calculations!