Light Beam - Minimum Travel Time
A beam of light travels through a compound dielectric slab along two straight line segments from the start point to the end point, as shown. The " " quantities are the speeds of the light beam in the two regions.
Suppose that the light travels along a path which minimizes the total travel time. When the light gets to the boundary between the two dielectric regions, what is its coordinate?
Inspired by a comment from Karan Chatrath
Note: As it turns out, this is actually how light behaves within a compound dielectric slab. From this "least time" principle, we can derive various well-known optical properties.
The answer is 4.2926.
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1 solution
3 1 √( x 2 +1)+ 2 1 √(( 6 − x ) 2 +4)=minimum. Therefore 5 x 4 -60 x 3 +173 x 2 -108x+324=0. The real solution to this equation less than 6 is x=4.29259