Is the Upper Optical Path Longer than the Lower One in Diagram 2?

[desmond iking]

Homework Statement

for diagram 2 , i just can't understand why S1P -t + ut (upper ray ) is longer than the lower light ray (S2P) , ? if I take S2P minus ( S1P -t + ut ) , then i would get mt t (thickness ) is negative , which is indeed wrong! so it has shown that optical path of the upper ray is longer than the optical path of lower ray ...

Homework Equations

The Attempt at a Solution

 

[mfb]

S1P - t + ut > S2P if u>1, as S2P=S1P based on the upper diagram. I guess u is your refractive index? Regular materials have a refractive index larger than 1, so the upper path is longer.