Question

How do you calculate the frequency of red light?

Answer 1

Hint: You could recall the numerous times you have calculated the frequency from the known values of wavelength and energy and hence the formulas used for the same. Now you could think of the range of wavelengths the visible light belongs to in the absence of the value of wavelength of light in the question. You could substitute them to get the required range.
Formula used:
Frequency,
$f=\dfrac{v}{\lambda }$

Complete answer:
In the question, we are asked as to how the frequency of red light could be measured.
We know that the frequency of any wave could be expressed in terms of velocity and wavelength as,
$f=\dfrac{v}{\lambda }$
Where, f is the frequency, v is the speed of the wave and $\lambda $ is the wavelength.
Frequency could be also expressed in terms of energy and Planck’s constant as,
$f=\dfrac{E}{h}$
Where, E is the energy and h is the Planck’s constant.
But unfortunately, we are given none of these quantities. But we know that the red light belongs to the visible range of the electromagnetic spectrum and they are found to be in the range of 620nm to 750nm in wavelengths. So we could find the corresponding frequency range.
${{f}_{\max }}=\dfrac{c}{\lambda }=\dfrac{3\times {{10}^{8}}}{620\times {{10}^{-9}}}$
$\therefore {{f}_{\max }}=4.84\times {{10}^{14}}Hz$
Also,
${{f}_{\min }}=\dfrac{3\times {{10}^{8}}}{750\times {{10}^{-9}}}$
$\therefore {{f}_{\min }}=4\times {{10}^{14}}Hz$
If we were given the wavelength or energy of red light we could have found the exact value of frequency of red light. But now we could only find the frequency range at which the frequency of red light may lie which is from $4\times {{10}^{14}}Hz$ to$4.84\times {{10}^{14}}Hz$.

Note:
While calculating we have substituted the universal speed of light in vacuum as it is known to be the speed at which electromagnetic waves propagate. Though we have found a narrow range where the frequency of red light may belong we could find the exact value if we had known its wavelength. Wavelength of red light is found to be $650nm$, so,
$f=\dfrac{3\times {{10}^{8}}}{650\times {{10}^{-9}}}=4.6\times {{10}^{14}}Hz$