NEET-XII-Physics
17: Light Waves
- #1Find the range of frequency of light that is visible to an average human being
400 nm <λ<700 nm.Ans : 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:
`` \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\,}``
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\,}``.
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