Question

How do you calculate the wavelength of light?

Answer 1

Hint: You may recall that the wavelength of the wave can be defined as the distance between two consecutive crests and troughs of a wave. You may have calculated this quantity many times. Also, calculation of a quantity largely depends on the known quantities. Now you may recall the expressions for wavelength of light in terms of energy and frequency.

Complete Step by step solution:
In the question, we are asked how to calculate the wavelength of light. Calculation of wavelength of light depends upon which quantity is already known of the light or which quantity’s value is already been given in the question.

The wavelength could be calculated from the known frequency of light. This is done using the following expression.
$\lambda ={\displaystyle \frac{c}{\nu }}$
Where, c is the universal speed of light in vacuum and $\nu$ is the known frequency of the light.

Other than this, we could also calculate wavelength, if the energy of the light is given instead of the frequency. This expression is derived by substituting the above expression in Planck’s equation.

Planck’s law states that the energy of a photon is directly proportional to its frequency and the Planck’s equation is given by,
$E=h\nu$
Where, E is the energy of the light and h is the Planck’s constant.

Substituting the above equation in Planck’s equation, we get,
$\lambda ={\displaystyle \frac{hc}{E}}$

Thus, we have found the two common ways to calculate the wavelength from the frequency and energy.

Note:
You may have noted the constants in the above found expressions for calculating wavelength of light. Universal speed of light in vacuum is known to have a value of,
$c=3\times {10}^{8}m{s}^{-1}$
Then we have the Planck’s constant that is known to have a value of,
$h=6.626\times {10}^{-34}J-\sec$