Question

In glass, light travels with a speed of 2.0 × 10^8 m/s. Light with a frequency of 3.6 × 10^14 Hz moves through the glass. What is the wavelength of the light?

Answer 1

Approximately
`5.56 * 10^(-7)\; {\rm m}` in this glass.

Step-by-step explanation:

The frequency of a wave is the number of periods that this wave completes per unit time.

The speed of a wave is the distance that this wave travels in unit time.

Thus, dividing the speed
`v` of the wave by the frequency
`f` of this wave would give the distance that this wave covers in each period (cycle) of this wave. By definition, the distance that a wave covers in each period is precisely the wavelength of this wave. Therefore, an equation for the wavelength
`\lambda` of a wave would be:

`\begin{aligned}\text{wavelength} &= \frac{\text{speed}}{\text{frequency}}\end{aligned}`.

`\begin{aligned}\lambda &= (v)/(f)\end{aligned}`.

Note that
`1\; {\rm Hz} = 1\; {\rm s^(-1)}`.

The wavelength of this light in this glass would be:

`\begin{aligned}\lambda &= (v)/(f) \\ &= \frac{2.0 * 10^(8)\; {\rm m\cdot s^(-1)}}{3.6 * 10^(14)\; {\rm s^(-1)}} \\ &\approx 5.56 * 10^(-7)\; {\rm m}\end{aligned}`.