Question

What is the frequency of a green light with a wavelength of $ 530 \times {10^{ - 9}}m $ ?

Answer 1

Hint :Use the relation between the speed of light, its frequency and wavelength to find the frequency of the given green light. Convert the given values into their respective S.I units before proceeding with the calculations.
For any electromagnetic wave, $ c = \nu \lambda $ , where $ c $ is the speed of the wave at vacuum, $ \lambda $ is the wavelength of the wave and $ \nu $ is the frequency of the wave.

Complete Step By Step Answer:
We know that light is the visible part of the electromagnetic spectrum and exhibits the wave nature. It actually exhibits dual behavior – both as a particle and as a wave. Since light is an electromagnetic wave it can be characterized by its wavelength, amplitude, frequency, wave number and speed of propagation. So, green light which is a part of the spectrum of visible light is also an electromagnetic wave.
It is given that the wavelength of the light $ \lambda = 530 \times {10^{ - 9}}m $ . Also, it is known to us that the speed of light is $ c = 3.8 \times {10^8}{m \mathord{\left/
 {\vphantom {m s}} \right.} s} $ .
We can now use the relation $ c = \nu \lambda $ to get $ \nu = \dfrac{c}{\lambda } $ .
So, the frequency of the green light would be $ \nu = \dfrac{{3.8 \times {{10}^8}{m \mathord{\left/
 {\vphantom {m s}} \right.} s}}}{{530 \times {{10}^{ - 9}}m}} $ .
 $ \Rightarrow \nu = 5.66 \times {10^{14}}{s^{ - 1}} $
 $ \Rightarrow \nu = 5.66 \times {10^{14}}Hz $
Hence, the frequency of green light with a wavelength of $ 530 \times {10^{ - 9}}m $ is $ 5.66 \times {10^{14}}Hz $ .

Note :
When substituting the values in the formula make sure that all of them are measured in the same system of units. Remember to better convert them into their respecting S.I units and then use it in the formula. For example, wavelength is expressed as nm, you have to convert it into its S>I unit m before proceeding with the calculations.