In this article, we will discuss the effect of refraction on wavelength while propagating from one medium to another, with detailed facts.
The frequency of the wave does not vary on refraction of the wave, hence, the wavelength of the wave is directly proportional to its speed. As the speed of the wave varies on traversing from mediums, the wavelength also shifts accordingly.
Does Refraction Affect Wavelength?
The refraction occurs when the ray of light travels from medium to another.
The velocity of the wave increases while traversing from the rarer mediums and decreases in denser mediums that determines the angle of refraction. The wavelength of the wave is relative to the velocity and varies parallelly.
We know that, the speed of the light c=λf. For any wave, propagating from two different mediums, moving with speed ‘v’ is directly proportional to the wavelength, as the frequency of the wave remains the same after refraction.
The velocity of the wave in the medium is directly dependent on the refractive index of the medium it is traversing through.
n1/n2 = v2/v1
v2/v1=λ2f/λ1f
As the frequency remains constant even after refraction,
v2/v1=λ2/λ1
Hence,
n1/n2=λ2/λ1
The refraction of the wave depends upon the wavelength and the wavelength is inversely proportional to the refractive index of the medium.
Read more on Types Of Refraction: Comparative Analysis.
How does Refraction Affect Wavelength?
The refraction may increase or decrease the wavelength of the light or sound propagating in the medium having higher density than the air.
When a wave travels in the denser medium the speed of the wave decreases and hence the wavelength decreases. The wavelength increases if the speed of the wave increases while traveling in a rarer medium.
Consider a wave propagating from rarer medium to denser medium and back to the rarer medium as shown in the below figure.
The velocity of the wave in the rarer medium is more and hence the wavelength of the wave is increased. On passing to the denser medium having a slightly greater refractive index, the speed of the wave and the wavelength reduces. On entering back to the rarer medium, the wavelength and speed of the wave increase.
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How does Index of Refraction Affect Wavelength?
The denser the medium, the velocity of the wave will decrease and hence the wavelength reduces.
The index of refraction is greater for the denser medium than the rarer because the speed and in proportionate the wavelength of the wave is reduced while traveling through the denser medium.
The refractive index of the medium is given as the velocities of the wave propagating from two different mediums. Suppose the light travels from medium 1 to medium 2, the refractive index of the medium is given as
n12=n1/n2=λ2/λ1
Where n1 is a refractive index of medium 1
n2 is a refractive index of medium 2
v1 is a velocity of light in medium 1
v2 is a velocity of light in medium 2
The speed of the wave is equal to the product of the wavelength and the frequency of the wave.
v=λ f
Let us take an example to clarify how does the wavelength of the wave depends upon the refractive index of the medium it is traveling through.
Read more on Refractive Index.
Example: Consider a wave of light propagating from air to water. If the frequency of the wave is equal to 6* 1016 /sec. Calculate the change in the wavelength of the light.
Given: f=6* 1016 /sec
Refractive index of air n1=1
Refractive index of water n2=1.33
n=c/v
n=c/λf
λ=c/nf
This shows that the wavelength is inversely proportional to the refractive index of the medium.
Wavelength of the light in air was
λ1=c/n1f
λ1=3* 108 / 1* 6 * 1016
λ1=5*107=500*10-9=500nm
After refraction, the wavelength of the light in water becomes
λ2=c/n2f
λ2=3* 108/ 1.33* 6* 1016
λ2=3.75* 10-7=375*10-9=375nm
It is clearly indicating that as the refractive index of the medium increased, the wavelength of the light decreased.
This implies that the speed of the light decreases in the medium having a greater refractive index, and increases while traversing from the medium of higher refractive index to lower refractive index.
Why does Wavelength Affect Refraction?
The refraction basically depends upon the density of the medium, and the temperature and pressure gradient of the medium.
As the density of the medium varies, the wavelength differs, and the direction of the propagation of the wave changes. If the wavelength increases, the angle of refraction will be greater.
When a wave travels from a denser to a rarer medium, the speed of light and hence the wavelength increases, and the refractive angle produced on bending the ray of light will be greater.
While a wave propagates from a rarer to a denser medium, the wavelength will decrease, and the refractive angle formed on bending the ray of light will be smaller.
Read more on How To Find Angular Acceleration From Angular Velocity: Problem And Examples.
Frequently Asked Questions
Why does the refractive index of glass is more than the air?
The refractive index is determined by the change in the speed of light while traversing from a given medium.
The speed of the light reduces to a greater extent in the glass compared to the speed of light in the air. Hence, the refractive index of a glass is more compared to air.
What will be the effect on the refraction if the frequency of the wave increased?
The frequency remains constant on refraction and is inversely correlated to the wavelength.
If the frequency increases then the speed of the wave will reduce, and the wave will divert towards the normal producing a small angle of refraction.
When does a ray of a light disperse after refraction?
If the white light traverses through the medium and emerges out at the same angle then the dispersion of light does not occur.
If all the components of the light emanating out from the medium at different angles then this phenomenon is called the dispersion of the light.
Why does the frequency of a light does not changes while propagating from higher density medium?
The speed of light decreases while traveling from the denser medium.
The frequency determines the propagation of light in time. As the speed reduces the wavelength will also shrink, thus the frequency remains constant.
Also Read:
- Frequency of a wave example
- How does a microwave vent work
- Types of sound waves
- Refraction of waves examples
- How are light waves produced
- Longitudinal wave example
- Sound wave equations
- Electromagnetic waves types
- How to calculate wave energy in ocean engineering
- How was the wave nature of light established
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.
