A swimming pool is filled with clear water (index 1.33). A scuba diver under the water shines a flashlight upward so that the emerging beam in the air forms an angle of exactly 60∘ with the normal to the water’s surface.
Work through the following multi-step analysis.
(a) Determine the angle that the light made with the normal while it was still traveling in the water.
(b) Using your result from part (a), calculate the angle that the diver must point the flashlight relative to the flat surface of the water (that is, measured from the horizontal plane of the surface).
(c) The diver rotates the flashlight so that the internal (water) angle you found in part (a) increases by 10∘. Predict qualitatively how the angle of the emerging beam in air changes, and support your prediction with quantitative reasoning using representative values.