Question

Find the frequency range of visible light, given that it encompasses wavelengths from \(380\) to \(760nm\)?

Short answer

The frequencyrange of visible light is \(395{\rm{ }}GHz\) to \(789{\rm{ }}GHz\).

Step-by-step solution

Definition of frequency

Frequency is the number of waves that pass through a specific spot in a specific length of time.

Given information and Formula to be used

The first wavelength is: \({\lambda _1} = 380\;nm = 0.38 \times {10^{ - 6}}\;m\)

The first wavelength is: \({\lambda _2} = 760\;nm = 0.76 \times {10^{ - 6}}\;m\)

The speed of light value is: \(c = 3 \times {10^8}\;m/s\)

For an electromagnetic wave, the relationship between propagation speed, wavelength, and frequency is given by,

\(c = f\lambda \)

Calculate the frequency

Consider the given formula and simplify,

We have

\(\begin{aligned} c &= {f_1}{\lambda _1}\\3 \times {10^8} &= {f_1} \times 0.38 \times {10^{ - 6}}\\{f_1} &= 789{\rm{ }}GHz\end{aligned}\)

\(\begin{aligned} c &= {f_2}{\lambda _2}\\3 \times {10^8} &= {f_2} \times 0.76 \times {10^{ - 6}}\\{f_2} &= 395{\rm{ }}GHz\end{aligned}\)

Therefore, frequency range from \(395{\rm{ }}GHz\) to \(789{\rm{ }}GHz\).