Question

Walter Light Wave and Percy Photon decide to have a race. Walter runs the entire race in air while Percy slogs his way through crown glass. If Walter beats Percy by 1.34E-6 s, how long was the race?

Answer 1

Question 37066

Walter Light Wave and Percy Photon decide to have a race. Walter runs the entire race in air while Percy slogs his way through crown glass. If Walter beats Percy by 1.34E-6 s, how long was the race?

A light wave and a photon are essentially the same thing due to the light dualism.

The difference in the travel time is due to the different refraction indices, $n_{W}=1$ for air (Walter) and $n_{P}=1.52$ for the crown glass (Percy). The speed of a photon in a given medium is $v=\frac{c}{n}$.

We are given information that $t_{P}-t_{W}=1.34\times 10^{-6}$ s.

If the length of the race is L, the travel times can be calculated as $t=\frac{L}{v}=\frac{Ln}{c}$.

This way the equation for time difference transforms into $\frac{L(n_{P}-n_{W})}{c}=1.34\times 10^{-6}$ s.

From this we can work out $L=\frac{(1.34\times 10^{-6}s)\times c}{(n_{P}-n_{W})}$.

Using the numerical values,

$L=\frac{(1.34\times 10^{-6}s)\times 3\times 10^{8}\frac{m}{s}}{(1.52-1.00)}\approx 773.08$ m.

Answer: about 773 m.