a) b) An cylindrical opaque drinking glass has a diameter 5.8 cm and height h, a

Question

a)

b)

An cylindrical opaque drinking glass has a diameter 5.8 cm and height h, as shown in the figure. An observer's eye is placed as shown (the observer is just barely looking over the rim of the glass). When empty, the observer can just barely see the edge of the bottom of the glass. When filled to the brim with a transparent liquid, the observer can just barely see the center of the bottom of the glass. The liquid in the drinking glass has an index of refraction of 1.37. Calculate the angle theta r. Answer in units of degrees Calculate the height h of the glass. Answer in units of cm

Explanation / Answer

Sin(Ai) = (d/2) / Sqrt((d/2)^2 + h^2)

Sin(Ar) = d/Sqrt(d^2 + h^2)

Snell's law:

1.37 Sin(Ai) = 1*Sin(Ar)

=> 1.37*[(d/2)/Sqrt((d/2)^2 + h^2)] = d/Sqrt(d^2 + h^2)

=> 0.47 [d^2 + h^2] = [(d/2)^2 + h^2]

0.22 d^2 = 0.53 h^2

=> 0.22 * 5.8^2 / 0.53 = h^2

=> h = 3.74 cm

tan Ar = d/h = 5.8/3.74 = 1.55

Ar = 57.21 degree

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