Please show me the steps to this problem. I\'m having a lot of trouble with it.

Question

Please show me the steps to this problem. I'm having a lot of trouble with it.

An cylindrical opaque drinking glass has a diameter 3.5 cm and height h, as shown in the ï¬gure. 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 ï¬lled 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 1.29.

A. Calculate the angle θr . Answer in units of degrees.

B. Calculate the height h of the glass. Answe in units of cm.

Explanation / Answer

a)

Suppose : Tr = y and Ti = x

1.29*sin(x) = sin(y) ==> x = arcsin((sin(y))/1.29)

2 tan(x) = tan(y) ===> y = arctan(2*tan(arcsin((sin(y))/1.29)))

y = (2*((((61.933)s)/1.29)is)t)it

==> y = 61.933 = 61.9 degrees

b)

tan(y) = d/h ===> h = d tan(y) = 3.5 * tan(61.933) = 6.56 cm

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