p35_016.pdf

16. First, we note that – relative to the water – the index of refraction of the carbon tetrachloride should be

thought of as n =1 . 46 / 1 . 33 = 1 . 1 (this notation is chosen to be consistent with problem 15). Now, if the

observer were in the water, directly above the 40 mm deep carbon tetrachloride layer, then the apparent

depth of the penny as measured below the surface of the carbon tetrachloride is d a =40mm / 1 . 1=

36 . 4 mm. This “apparent penny” serves as an “object” for the rays propagating upward through the

20 mm layer of water, where this “object” should be thought of as being 20 mm + 36 . 4mm = 56 . 4mm

from the top surface. Using the result of problem 15 again, we ﬁnd the perceived location of the penny,

for a person at the normal viewing position above the water, to be 56 . 4mm / 1 . 33 = 42 mm below the

water surface.