Question

What is the wavelength (in nm) of the red light emitted by a barcode scanner that has a frequency of $4.62 \times {10^{14}}\,{s^{ - 1}}$ ?

Answer 1

In order to solve this question, we need to understand wavelength and frequency. Wavelength of light is defined as consecutive distance between crest and consecutive trough of wave. Frequency of the light is defined as the number of revolutions that a wave makes in each cycle. In the solutions, we would establish a relation between wavelength, frequency, and light speed. Then we put the values to get the final value. Also barcode is a special letter which absorbs a certain frequency of light and reflects others, which is then read by a barcode scanner.

Complete step by step answer:
Let the wavelength of light be, $\lambda$. Also, let the frequency of light used is,
$v = 4.62 \times {10^{14}}{s^{ - 1}}$
Let the light speed be denoted as,
$c = 3 \times {10^8}m{\sec ^{ - 1}}$
We know the relation between wavelength, frequency and light speed as,
$\lambda v = c$
So the wavelength is,
$\lambda = \dfrac{c}{v}$
Putting values we get,
$\lambda = \dfrac{{3 \times {{10}^8}m{{\sec }^{ - 1}}}}{{4.62 \times {{10}^{14}}{{\sec }^{ - 1}}}}$
$\Rightarrow \lambda = 0.649 \times {10^{ - 6}}\,m$
Since $1\,nm = {10^{ - 9}}\,m$
So the meter can be expressed in terms of nanometer as, $1\,m = {10^9}\,nm$
So wavelength in terms of nanometer is,
$\lambda = (0.649 \times {10^{ - 6}}) \times ({10^9})\,nm$
$\therefore \lambda = 649\,nm$

So the wavelength (in nm) of the red light emitted by a barcode scanner is, $649\,nm$.

Note: It should be remembered that frequency is a fundamental property of a wave, it only changes when the time period of wave changes, while both the wavelength and speed are non-fundamental properties of the wave as it depends on material medium in which the wave is travelling. Both the wavelength and speed of light depends on the refractive index of the material medium.