Physics · Ch 6 — Optics

Optical Path

6.3.4

Optical Path

The optical path of a medium is the distance $d'$ that light would travel in vacuum in the same time that it actually takes to cross a real distance $d$ through that medium. If light of speed $v=c/n$ takes time $t=d/v$ to cross a medium, it could, in that same time $t$ , have travelled the (longer) distance $d'=ct=nd$ in vacuum, where it moves at the higher speed $c$ . So $\boxed{d'=nd}$ . Since $n>1$ for every real transparent medium, the optical path $d'$ is always greater than the actual geometric path $d$ -- physically, inserting a medium into a light beam's path effectively 'costs' an extra optical-path length of $(n-1)d$ , even though the beam's real physical travel distance is unchanged. This idea of counting distances in equivalent-vacuum units, rather than raw ph …

Figure 6.14Optical path

What this figure shows. A slab of thickness d and refractive index n is shown alongside an equal time interval spent by light travelling in vacuum, where -- because vacuum light travels faster -- it covers a longer distance d' = n d instead. The diagram visually anchors why the optical path is always the larger of the two numbers: the same elapsed time buys less physical distance inside the slower, denser m …

Misc Example 6.6Speed, transit time and optical path for light crossing a glass slab

Worked out. Light enters a glass slab of thickness 50 cm (0.5 m) and refractive index 1.5. Its speed inside the glass is v = c/n = (3 times 10 to the 8)/1.5 = 2 times 10 to the 8 metres per second. The time it takes to cross the slab is t = d/v = 0.5/(2 times 10 to the 8) = 2.5 times 10 to the -9 seconds. The optical path is d' = nd = 1.5 times 0.5 = 0.75 m = 75 cm -- 25 cm longer than the slab's actual 50 cm thickness, meaning light would have travelled 25 cm farther in vacuum during that same 2.5 nanoseconds had the glass slab not been there to …

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