Effect Of Refraction On Frequency: How, Why Not, Detailed Facts


In this article, we will discuss the effect of refraction on frequency, how does the frequency is affected by refraction, with detailed facts.

As a wave propagates from one medium to another, the speed of a wave changes, and hence the wavelength also varies. Due to this, the wave changes its direction of propagation making an angle of refraction.

What is Refraction?

A wavelength of light, sound, or any vibrations that traverse inside the medium is called refraction.

On refraction, the direction of the wave changes and propagates at an angle of refraction depending upon the density, temperature, and pressure gradient of the medium.

Read more on Types Of Refraction: Comparative Analysis.

Does Refraction Affect Frequency?

A wave of a certain amplitude propagating from two different mediums, the amplitude of wavelength varies depending upon the density of the medium through which it travels.

If the wave travels from a rarer to a denser medium, the speed of the wave decreases and the amplitude of the wavelength also diminishes. The same is reversed when a wave travels from denser to the rarer medium.

The speed of the wave is given by the equation

Speed=Frequency*Wavelength

v=f*λ

Where v is a speed of a wave

f is a frequency of the wave

λ is a wavelength

As the speed of the wave increases or decreases, the wavelength also increases or decreases respectively, and hence the frequency of the wave remains unchanged.

Consider a wave traveling from two different mediums. Let n2>n1, that second medium be denser than medium 1.

Effect of refraction on frequency
Variation in wavelength during propagation from two different mediums

As the wave propagates from medium 1 having refractive index n1 to medium 2 with refractive index n2, the speed of the wave decreases because medium 2 is denser than medium 1 and the amplitude of the wave also reduces. Again, as the wave passes back to the previous medium, that is from denser to rarer medium, the wavelength and the speed of the wave increase back. In the process, the frequency of occurrence of the nodes of the wave remains the same.

Read more on What Is Oscillation Frequency: Interesting Facts and FAQs.

Does Index of Refraction affect Frequency?

The index of refraction determines the angle of refraction while traversing from one medium to another.

The speed of the wave in the medium depends upon the refractive index of that medium, but the frequency of the wave remains unaffected by the refractive index.

The refractive index of the medium is stated by the equation as

n=c/v

Where n is a refractive index of the medium

c is a speed of light, c=3* 108m/s

v is a speed of light in medium

If the speed of the light decreases while propagating from the medium then this implies that the index of refraction is greater than 1.

In a vacuum, the speed of light remains the same and therefore the refractive index of the vacuum is one, and a ray of light travels making 1800 angle.

If the refractive index of the medium is greater than 1 then the wavelength of the wave reduces; and while traveling from denser to rarer medium, the wavelength increases, but the frequency of the wave remains the same.

Read more on Refractive Index.

Is Refraction Affected by Frequency?

The frequency of the wave does not change after refraction.

The refractive index of the wave is directly proportional to the permittivity of the medium and determines how fast the wave can travel through the medium. The permittivity depends upon the frequency of wavelength in the medium.

We can talk about the permittivity of the medium based on the density that significantly decides the velocity of the wave in the medium. In a rarer medium, permittivity will be more because the frequency of the light will be reduced as the wavelength will increase. The velocity of the wave will increase hence the refractive angle will be more.

In a medium having less permittivity, the frequency of the wave propagating from the medium will be more, hence the wavelength will be less, the velocity of the wave will decrease and the wave will refract at the smaller angle. This is in the case of a denser medium.

Why does refraction not affect Frequency?

The frequency of the wave propagating from different mediums does not change.

The energy of the wave is conserved before and after the refraction, which implies that the frequency of the wave remains unaffected.

The energy associated with the wave is given by the equation

E=hf=hv/λ

As the speed of the wave increases or decreases based on the permittivity of the medium, the wavelength of the wave also increases or decreases respectively, and therefore the frequency remains unaffected.

Speed is directly proportional to the wavelength propagating in space. While propagating from mediums having different densities, the speed, the amplitude, and hence the wavelength of the wave differs, but the number of waves occurring per unit time remains the same even after refraction.

Read more on Can Light Bend Around Corners? Important FAQs.

Does Frequency Affect Angle of Refraction?

The angle of refraction depends upon the change in the speed of the wave varied while traveling from one medium to another.

Based on the density of the medium the speed of wave varies and diverts at a particular angle on refraction.

Consider a light wave is propagating from air to glass then the refractive index of the medium is given by Snell’s Law as

nair/nglass=sinθr/sinθi

The refractive index is directly proportional to the speed of the wave in different mediums while propagating, then

nair/nglass=v2/v1

Hence,

v2/v1=sinθr/sinθi

The angle of refraction depends upon the speed of light after refraction and the angle of incident depends upon the speed of the incident light.

As, the speed is product of the wavelength and the frequency, we can write

v2/v12f1f

Frequency of the light remains the same after refraction, therefore,

v2/v12f1f

That is,

sinθr/sinθi=v2/v121

For a constant wavelength, the velocity of the wave will increase by increasing the frequency of the wave, and the wave will refract at a greater angle after refraction. If the frequency is less, then the speed of the wave will be deduced and the refractive angle will be smaller.

Read more on Spherical Mirror | All Important concepts and 10+ FAQs.

Frequently Asked Questions

Does the wavelength of the light vary in the vacuum?

The wavelength of the light directly corresponds to the speed of the light.

The speed of the light does not change while traveling through a vacuum, that is v=c, hence the refractive index n= c/v = 1. Since v remains constant, the wavelength is also constant.

Does the temperature affect the refraction of the light?

The refraction of the light depends upon the refractive index, the density, the permittivity of the medium, and the temperature too.

If the temperature rises then the density of the medium drops and the speed of the wave in the medium will increase. Hence, the refracted ray will get diverted making a greater angle with normal.

AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn - linkedin.com/in/akshita-mapari-b38a68122

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