Question

A submarine is 306 m horizontally out from the shore and 110 m beneath the surface of the water. A laser beam is sent from the sub so that it strikes the surface of the water at a point 218 m from the shore. If the beam just strikes the top of a building standing directly at the water's edge, find the height of the building.

Answer 1

the angle of incidence of the light ray in the water can be found (using trigonometry) to be
tan^-1([306-218]/110) = tan^-1(88/110) = 38.66 degrees.

Using Snell's Law, with the refractive index of water being 1.333 and the refractive index of air being 1, we can find the angle of refraction into the air to be
sin^-1(1.333sin38.66) = 56.185 degrees, and using trigonometry, we can find the height of the building must be

218/tan56.185 = 146 m.