Question

Find the range of frequency of light that is visible to an average human being $\left(400\mathrm{nm}<\lambda <700\mathrm{nm}\right)$.

Answer 1

Given:
Range of wave length is
$400\mathrm{nm}<\lambda <700\mathrm{nm}$
We know that frequency is given by $f=\frac{c}{\lambda }$,
$\mathrm{where}\mathrm{c}=\mathrm{speed}\mathrm{of}\mathrm{light}=3\times {10}^8\mathrm{m}/\mathrm{s}$
f is the frequency
λ is the wavelength
We can write wavelength as:
$$\begin{gathered} \frac{1}{700\mathrm{nm}}<\frac{1}{\lambda }<\frac{1}{400\mathrm{nm}} \\ \Rightarrow \frac{1}{7\times {10}^{-7}\mathrm{m}}<\frac{1}{\lambda }<\frac{1}{4\times {10}^{-7}\mathrm{m}} \\ \frac{3\times {10}^8}{7\times {10}^{-7}}\mathrm{Hz}<\frac{c}{\lambda }<\frac{3\times {10}^8}{4\times {10}^{-7}}\mathrm{Hz} \\ \Rightarrow 4.3\times {10}^{14}\mathrm{Hz}<\frac{c}{\lambda }<7.5\times {10}^{14}\mathrm{Hz} \\ \Rightarrow 4.3\times {10}^{14}\mathrm{Hz}<f<7.5\times {10}^{14}\mathrm{Hz} \end{gathered}$$

Hence, frequency of the range of light that is visible to an average human being is $4.3\times {10}^{14}\mathrm{Hz}\mathrm{to}7.5\times {10}^{14}\mathrm{Hz}$.