A beam of light originates in a freshwater lake (nwater=1.33) and strikes the flat surface of a glass pane (nglass=1.50) at an incident angle of 60∘ measured from the normal in the water. The opposite face of the pane is directly exposed to air (nair=1.00) and is parallel to the first face. The thickness of the glass is sufficiently large that the two interfaces can be treated independently.
(a) Calculate the angle the beam makes with the normal while traveling inside the glass.
(b) Using your result from part (a), determine whether the beam is transmitted into the air or totally internally reflected at the glass–air boundary. Provide quantitative evidence for your conclusion.
(c) Suppose the lake water is replaced with seawater of index 1.36, while all other parameters remain unchanged. Repeat parts (a) and (b) conceptually and state whether your earlier conclusion about transmission versus total internal reflection changes, explaining why.
(d) Generalize your reasoning to describe the range of external incidence angles in water that would lead to total internal reflection at the glass–air interface for the original freshwater case.