Question

Speed of light in vacuum is $3\times {10}^8\text{m/s}$. The range of wavelength of visible light is $4000{\text{A}}^{\circ }-7000{\text{A}}^{\circ }$. Then, what will be the range of frequency of visible light?

• A. $2.14\times {10}^{14}\text{Hz}-7.5\times {10}^{14}\text{Hz}$
• B. $4.28\times {10}^{14}\text{Hz}-7.5\times {10}^{14}\text{Hz}$
• C. $4.28\times {10}^{14}\text{Hz}-5\times {10}^{14}\text{Hz}$
• D. $4.28\times {10}^{15}\text{Hz}-7.5\times {10}^{10}\text{Hz}$

Answer 1

The correct option is B $4.28\times {10}^{14}\text{Hz}-7.5\times {10}^{14}\text{Hz}$

We know, if $f$ = frequency, $\lambda$ = wave length and $v$ = speed of light in vacuum.
then, $v=f\lambda$ or $f=\frac{v}{\lambda }$

So, for maximum frequency, $f_{max}=\frac{v}{{\lambda }_{min}}$

Substituting the given data,

$f_{max}=\frac{3\times {10}^8}{4000\times {10}^{-10}}=7.5\times {10}^{14}\text{Hz}$

and minimum frequency, $f_{min}=\frac{v}{{\lambda }_{max}}$

Substituting the given data,

$f_{min}=\frac{3\times {10}^8}{7000\times {10}^{-10}}=4.28\times {10}^{14}\text{Hz}$

So, Range of frequencies pf visible light will be $[4.28\times {10}^{14}\text{Hz}-7.5\times {10}^{14}\text{Hz}]$

Hence, option (b) is the correct answer.


$\begin{array}{c}\text{Why this Question}?\\ \text{This question teaches the student how to use the relation between frequency and wavelength.}\\ \text{It also introduces the concept of visible light as a subset of the electromagnetic spectrum}\end{array}$