Question

A monochromatic light wave in vacuum has frequency f0 and wavelength λ0. Which of the following are also possible frequency and wavelength combinations for a monochromatic light wave in vacuum?

None of the above

2f0, λ0/2

f0/2, λ0/2

2f0, 2λ0

Answer 1

Option 2: 2f0 and λ0/2

Step-by-step explanation:

The relationship between frequency and wavelength of a wave is given by

f0 = c/λ0

Where f0 is the frequency, λ0 is the wavelength and c is the speed of light assuming the speed of light remains constant so the relationship becomes

f0 = 1/λ0

As you can see they have a inverse relationship and we can prove mathematically that option 2 is correct

f0 = 1/λ0

Multiply both sides by 2

2f0 = 2/λ0

which can also be written as

2f0 = 1/λ0/2

So the combination is (2f0 and λ0/2)

similarly, divide both sides by 2

λ0/2 = 1/2f0

So the combination is (λ0/2 and 2f0)

Therefore, option 2 is correct if frequency is 2f0 then corresponding wavelength would be λ0/2