Speed of Light in Media

Light travels at $c = 3 \times 10^8\,\text{m/s}$ in vacuum. Inside a transparent medium, it slows down. The ratio of the vacuum speed to the medium speed defines the refractive index:

$n = \frac{c}{v} \quad \Longrightarrow \quad v = \frac{c}{n}$

Speed in Various Media

Wavelength Change

Light's frequency $f$ does not change when it enters a medium (it's set by the source). But since $v = f\lambda$, a lower speed means a shorter wavelength:

$\lambda_n = \frac{\lambda_0}{n}$

Where $\lambda_0$ is the wavelength in vacuum and $\lambda_n$ is the wavelength in the medium.

Example: Yellow sodium light ($\lambda_0 = 589\,\text{nm}$) entering glass ($n = 1.5$):

$\lambda_n = \frac{589}{1.5} \approx 393\,\text{nm}$

The wavelength shortens, but the color we perceive is determined by frequency — so the light still looks yellow when it exits.

Finding the Refractive Index

If you measure the speed of light inside a medium:

$n = \frac{c}{v}$

Your Task

Implement the three functions below. Use $c = 3 \times 10^8\,\text{m/s}$.