Question

Calculate the frequency of yellow light of wavelength 550 nm. The speed of light is $3\times {{10}^{8}}m/s$ .
A. $5.4\times {{10}^{11}}Hz$
B. $5.4\times {{10}^{14}}Hz$
C. $2.7\times {{10}^{14}}Hz$
D. $2.7\times {{10}^{11}}Hz$

Answer 1

The frequency $f$ of light is related to the wavelength $\lambda$ as given below,
$f=\dfrac{c}{\lambda }$
Where, $c=3\times {{10}^{8}}m/s$ the speed of light in vacuum.

Complete step by step answer:
You have given the wavelength $\lambda$ of light, $\lambda =550nm$
The speed of light $c=3\times {{10}^{8}}m/s$
You have to find the frequency of light $f$
Before proceeding for calculation, we have to check the units,
Here speed is given in m/s, so you should convert wavelength in m.
You know, $1nm={{10}^{-9}}m$
So, $550nm=550\times {{10}^{-9}}m$
Therefore, $\lambda =550\times {{10}^{-9}}m$

The frequency $f$ is given by the below formula,
$f=\dfrac{c}{\lambda }$
Put the given values,
$f=\dfrac{3\times {{10}^{8}}m/s}{550\times {{10}^{-9}}m}$
Calculate,
$\begin{aligned} & f=\dfrac{3}{55}\times {{10}^{16}} \\\ & =0.054\times {{10}^{16}} \\\ & =5.4\times {{10}^{14}}Hz \end{aligned}$

So, the correct answer is “Option B”.

Additional Information:
1. The frequency of light doesn’t change when it passes through the different medium. But the wavelength and speed of light does change as it passes through the different mediums.
Then, you are going to use this below formula for wavelength,
$\lambda =\dfrac{c}{f}$
Where, $c$ is speed of light in medium, $f$ is the frequency of light.
2. Light always propagates in a straight line.
3. The wavelength generally denoted in units nm, pm, ${{A}^{0}}$. You should know all these units also conversion of units from one to another. For that always remember unit in m
i.e.
$\begin{aligned} & 1nm={{10}^{-9}}m \\\ & 1pm={{10}^{-12}}m \\\ & 1{{A}^{0}}={{10}^{-15}}m \\\ \end{aligned}$
If a question gives value in nm and asks an answer in pm then you should follow these steps.
First convert question value to m then convert to pm.

Note:
If you have given the speed of light in medium then use that speed instead of speed of light in vacuum c. Always check the units.