Refraction, wavelength and frequency

[Gajan1234]

I've learned that when wavelength increase the frequency decreases.

But in Refraction, there is a mention about frequency remains same but the wavelength and speed changes. Why does the frequency doesn't change? I thought when when wavelength is short the peaks are closer to each other so there will be more cycles per second.

 

[Buzz Bloom]

when wavelength increase the frequency decreases.

Hi Gajan:

The rule above is not for a single photon but relates to comparing properties of different photons moving at the same speed.
One form of the relevant equation is:

wavelength × frequency = speed.​

When a photon slows down moving through some medium, the frequency is unchanged, so the wavelength is then proportional to the speed.

Hope this helps.

Regards,
Buzz

 

[blue_leaf77]

The two statements above are unrelated.

I've learned that when wavelength increase the frequency decreases.

There, you are talking about the spectrum of the electromagnetic wave. In vacuum, rgardless of its frequency or wavelength, EM wave propagates with the speed of $c=3\times 10^8$ m/s. The frequency and wavelength are related through $c=\lambda f$. So, obviously in order to keep $c$ fixed, $\lambda$ and $f$ must change in a reciprocal way.

But in Refraction, there is a mention about frequency remains same but the wavelength and speed changes. Why does the frequency doesn't change? I thought when when wavelength is short the peaks are closer to each other so there will be more cycles per second

In the linear regime, which is applicable in most cases, the transmitted/refracted light has the same frequency as the incoming one because the substance making up the medium response linearly. This means, if the incoming light has a frequency $f$, the atoms or molecules inside the medium also oscillates with a frequency of $f$, radiating a secondary wave with frequency $f$. The wavelength, however, must change because each emitter (the atoms/molecules) must radiate such that all emitted waves superimpose constructively. Mathematical analysis shows that this so-called phase matching between the emitters requires that the wavelength be different from that of the incoming wave.

 

[Khashishi]

Light is a wave. In a beam there is a continual train of peaks and valleys. When light transitions to a region of higher index of refraction, the rate at which peaks come into the region doesn't change. Instead they bunch up more. Think about it. If the frequency of peaks was lower coming out of the region than coming in, either peaks would have to continually build up in the juncture or the output wave would have to become decorrelated with the input wave.

 

[Gajan1234]

Light is a wave. In a beam there is a continual train of peaks and valleys. When light transitions to a region of higher index of refraction, the rate at which peaks come into the region doesn't change. Instead they bunch up more. Think about it. If the frequency of peaks was lower coming out of the region than coming in, either peaks would have to continually build up in the juncture or the output wave would have to become decorrelated with the input wave.

I am quite confused, does this means that the wavelength will bot change as well.

 

[Gajan1234]

Hi Gajan:

The rule above is not for a single photon but relates to comparing properties of different photons moving at the same speed.
One form of the relevant equation is:

wavelength × frequency = speed.​

When a photon slows down moving through some medium, the frequency is unchanged, so the wavelength is then proportional to the speed.

Hope this helps.

Regards,
Buzz

Are we not viewing light as wave in this case?

 

[Khashishi]

The wavelength changes. The frequency does not change.

 

[Gajan1234]

The wavelength changes. The frequency does not change.

so where do we apply the rule that the frequency changes when wavelength is changed

 

[Khashishi]

Frequency changes in the case of Doppler shift or gravitational redshift. This is due to the relativity of time and had nothing to do with traveling through media.

 

[jbriggs444]

so where do we apply the rule that the frequency changes when wavelength is changed

If speed is constant, frequency changes when wavelength is changed.

 

[GadgetStrutter]

The wavelength is inversely proportional to the frequency, $$ƒ = \frac{cycles}{time} \ \ \ \ λ = \frac{time}{cycles}$$ So this relationship basically means that $$λ = \frac{1}{ƒ} \ \ \ \ \ \ \ λ = \frac{c}{ƒ}$$ $$c = λƒ \ \ \ \ \ \ v = λƒ$$ This means that the velocity is equal to the product of the wavelength and it's frequency. If the frequency remains constant and the wavelength changes, it means that the speed would increase or decrease in order to compensate for the cycles over time.​

 

[DrDu]

I've learned that when wavelength increase the frequency decreases.

This is true as long as you compare waves moving either in vacuum or in the same medium. However, in media, the speed of light is different than the speed of light in vacuum. In general, $f=c_0 n/\lambda$, where f is frequency, $c_0$ is the speed of light in vacuum and $\lambda$ is the wavelength. The index of refraction, n, is typically a function of frequency itself, so that the relation between frequency and wavelength becomes non-linear. This is called dispersion.
In refraction, you consider a situation where light changes from one medium to another. In this situation, frequency stays constant, but the wavelength changes due to the different indices of refraction of the media into question.