Question

Find the range of frequency of light that is visible to an average human being

\[\left( 400\text{ nm }< \lambda < 700\text{ nm}\right)\]

Answer 1

Given:-

Range of wave length is \[\left( 400\text{ nm }< \lambda < 700\text{ nm}\right)\]

We know that frequency is given by \[f = \frac{c}{\lambda}\]

\[\text{where c = speed of light} = 3 \times {10}^8 m/s\]

f is the frequency

λ is the wavelength

We can write wavelength as

\[\frac{1}{700\text{ nm}} < \frac{1}{\lambda} < \frac{1}{400\text{ nm}}\]

\[ \Rightarrow \frac{1}{7 \times {10}^{- 7} m} < \frac{1}{\lambda} < \frac{1}{4 \times {10}^{- 7} m}\]

\[\frac{3 \times {10}^8}{7 \times {10}^{- 7}} \text{Hz} < \frac{c}{\lambda} < \frac{3 \times {10}^8}{4 \times {10}^{- 7}} \text{Hz}\]

\[ \Rightarrow 4 . 3 \times {10}^{14} \text{Hz} < \frac{c}{\lambda} < 7 . 5 \times {10}^{14} \text{Hz}\]

\[ \Rightarrow 4 . 3 \times {10}^{14} \text{Hz} < f < 7 . 5 \times {10}^{14} \text{Hz}\]

Hence, frequency of the range of light that is visible to an average human being is \[4 . 3 \times {10}^{14} \text{Hz to }7 . 5 \times {10}^{14} \text{Hz}\]