When light waves traveling in a transparent medium strike the surface of a second transparent medium, they change direction. This change of direction is called refraction and is defined by Snell’s Law of Refraction,

where θ₁ and θ₂ are the magnitudes of the angles shown in the figure and v₁ and v₂ are the velocities of light in the two media. Show that this problem is equivalent to that in Exercise 42, and that light waves traveling from P to Q follow the path of minimum time.

Data from in Exercises 42

The conditions are the same as in Exercise 41 except that the man can row at v₁ miles per hour and walk at v₂ miles per hour. If θ₁, and θ₂ are the magnitudes of the angles, show that the man will reach point Q in the least time when

Transcribed Image Text:

sin 0, V₁ sin 0, V2