Question

What is the speed of a visible light wave if the wavelength is $4\times {{10}^{-7}}$ m and frequency $7.5\times {{10}^{14}}$ Hz?

Answer 1

Hint: There is a formula to calculate the speed of the light by using wavelength and frequency of the light and it is as follows.
\[\begin{align}
  & v=\frac{c}{\lambda } \\
 & c=v\lambda \\
\end{align}\]
Here c =speed of the light
$v$ = frequency of the light
$\lambda $ = wavelength of the light

Complete answer:
- In the question it is asked to calculate the speed of the visible light by using the given data in the question.
- The given data is, wavelength of the light is $4\times {{10}^{-7}}$ m and frequency of the visible light is $7.5\times {{10}^{14}}$ Hz.
- The relationship between speed of the light, frequency of the light and wavelength is as follows.
\[\begin{align}
  & v=\frac{c}{\lambda } \\
 & c=v\lambda \\
\end{align}\]
Here c = speed of the light
$v$ = frequency of the light = $7.5\times {{10}^{14}}$ Hz.
$\lambda $ = wavelength of the light = $4\times {{10}^{-7}}$ m
- Substitute the known values in the above to get the speed of the visible light and it is as follows.
\[\begin{align}
  & v=\frac{c}{\lambda } \\
 & c=v\lambda \\
 & c=4\times {{10}^{-7}}\times 7.5\times {{10}^{14}} \\
 & c=3\times {{10}^{8}}m/\sec \\
\end{align}\]
- Therefore the speed of the visible light with a frequency $7.5\times {{10}^{14}}$ Hz. And wavelength $4\times {{10}^{-7}}$ m is $3\times {{10}^{8}}m/\sec $ .

Note:
As the wavelength increases the frequency of the light is going to decrease. This is because the wavelength is inversely proportional to the frequency of the light. We can express the frequency in hertz or per second also. The relation between hertz and per second is as follows.
1 Hz = $\frac{1}{s}={{s}^{-1}}$
Without knowing the wavelength and frequency of the visible light we cannot determine the speed of the visible light.