Question

One light beam has wavelength, and frequency, fl. Another light beam has wavelength, in, and frequency, f2. Write a proportion that shows how the ratio of the wavelengths of these two light beams is related to the ratio Of their frequencies.

Answer 1

The question is missing. Here is the complete question.

One light beam has wavelength, $\lambda_{1}$, and frequency, f₁. Another light beam has wavelength, $\lambda_{2}$, and frequency, f₂. Write a proportion that shows how the ratio of the wavelengths of these two light beams is related to the ratio of the frequencies.

Answer: $\frac{f_{1}}{f_{2}} =\frac{\lambda_{2}}{\lambda_{1}}$

Explanation: In vacuum, eletromagnetic waves travels at a constant speed called "speed of light", whose symbol is [c] and magnitude is 3x10⁸m/s.

Speed of light, frequency and wavelength are related by the formula:

$c=\lambda.f$

So, if one light beam has wavelength and frequency, $\lambda_{1}$ and f₁, respectively, the second beam has wavelength $\lambda_{2}$ and frequency f₂ and both travel at speed of light:

$\lambda_{1}f_{1}=\lambda_{2}f_{2}$

$\frac{f_{1}}{f_{2}}=\frac{\lambda_{2}}{\lambda_{1}}$

Then, the ratio that shows the relation between frequencies and wavelengths of these light beams is $\frac{f_{1}}{f_{2}}=\frac{\lambda_{2}}{\lambda_{1}}$