How to Find the Wavelength of Light Using its Frequency

How to Find the Wavelength of Light Using its Frequency

When finding the wavelength of light using its frequency, follow these easy steps:

Step 1: Read the Problem

Step 2: Take the information provided within the problem and plug it into the wavelength equation to determine the wavelength .

What is a Wave?

A wave can be expressed as an oscillation carrying energy from one point to another through space and time.

What is a Wavelength?

A wavelength is defined as the distance between two successive wave peaks, the highest points of the wave, or two successive troughs, the lowest points of the wave.

What is Frequency?

Wave frequency describes the number of waves passing through a fixed point over a specific amount of time.

How to Find the Wavelength of Light Using its Frequency

When given the frequency of a wave, one can use the following formula to determine the wavelength:

{eq}\lambda = \frac{v}{f} {/eq}

Where {eq}\lambda {/eq} is the wavelength which is measured in meters, v is the velocity of the wave measured in meters per second (m/s), and f is the frequency of the wave which is measured in Hertz (Hz).

This formula can be used when two out of the three variables are given

However, if only one variable is provide, you can use the following formula:

{eq}\lambda = \frac{c}{f} {/eq}

Where {eq}\lambda {/eq} is the wavelength which is measured in meters, c is the speed of light which equals {eq}3 \times 10^{8} {/eq} m/s, and f is frequency which is measured in Hertz (Hz).

Examples of Determining Wavelength from Frequency

The following examples will help illustrate how to determine wavelength from frequency.

Example 1

If the frequency of light is {eq}4.7 \times 10^{8} {/eq} Hz, what will its wavelength be?

Step 1: Read the Problem

After reading the problem, we can see that only one variable is given. Therefore, we know that we can use the formula

{eq}\lambda = \frac{c}{f} {/eq}

Step 2: Take the information provided within the problem and plug it into the wavelength equation to determine the wavelength

Now we can plug the values we have into the equation and solve for lambda which is wavelength.

{eq}\lambda = \frac{3 \times 10^{8} m/s }{4.7 \times 10^{8} Hz} = 0.64 m {/eq}

Example 2

What will the length of the light wave be, if the frequency is {eq}2.4 \times 10^{8} {/eq} Hz and its velocity is indicated to be {eq}2.6 \times 10^{8} {/eq} meters per second?

Step 1: Read the Problem

After reading the problem, we can see that two variables are given. Therefore, we know that we can use the formula

{eq}\lambda = \frac{v}{f} {/eq}

Step 2: Take the information provided within the problem and plug it into the wavelength equation to determine the wavelength

Now we can plug the values we have into the equation and solve for lambda which is wavelength.

{eq}\lambda = \frac{2.6 \times 10^{8} m/s }{2.4 \times 10^{8} Hz} = 1.08 m {/eq}