Calc Angle of Refraction in Opaque Drinking Glass Problem

[U154756]

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]

**Bump**

I would like to know if anyone has found a way to solve this.

Please help.

-U

 

[astrokreng]

I would first start by defining the problem and identifying the relevant variables. In this case, we are dealing with a cylindrical opaque drinking glass with a diameter of 4.7 cm and a height h. The observer's eye is placed just barely looking over the rim of the glass, and the observer can barely see the edge of the bottom of the glass when it is empty and the center of the bottom when it is filled to the brim. The liquid in the glass has an index of refraction of 1.29.

To solve this problem, we can use Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two mediums. However, as the poster mentioned, we need to know one of the angles in order to use this equation.

In this case, we can use the fact that the observer's eye is just barely looking over the rim of the glass to determine the angle of incidence. This angle would be equal to the angle between the observer's eye and the horizontal plane. We can also use the height of the glass and the diameter to determine the angle of refraction using basic trigonometry.

Once we have both angles, we can use Snell's law to calculate the angle of refraction in the liquid, and from there, we can determine the angle at which the observer is looking into the glass.

In summary, to solve this problem, we can use Snell's law and basic trigonometry to determine the angle at which the observer is looking into the glass. It is important to define the problem clearly and identify the relevant variables before attempting to solve it.