Physics 102
Practice Exam Problem #12

From an underwater lagoon in Nassau, Prof. Roelofs was able to see the base of a building located some distance from the lagoon. Had this light travelled in a straight line from the building to his eyes it would have had to pass through the earth rather than through water. The sketch shows light leaving from near the base of the building and so he would have been unable to see that part of the building. The dashed line is a straight line to Prof. Roelofs, and one sees that it would be stopped by the intervening earth. The solid line shows the path actually followed by the light.

(a) Suppose the angle made by the light leaving the building is 2¡ relative to the horizontal. At what angle upward, again relative to the horizontal, is Prof. Roelofs looking in order to see the base of the building? Take the index of refraction of the water in the lagoon to be n=1.33. (Note that angles of incidence and refraction are conventionally defined relative to an axis perpendicular to the interface. Such an axis has been included in the figure for your convenience.)

(b) What does Prof. Roelofs see if he looks at a slightly lower angle relative to the horizontal?

(Problem from an actual former Physics 102 exam)
Solution

Physics 102 HW page