Refractive Index Formula

What is the Refractive Index Formula?

The refractive index of a medium is the measurement of how light bends when it passes through a medium to another medium. Refractive index can be defined as the ratio of the speed of light in a medium to the speed of light in a vacuum. Here you will learn about different types of the angle of refraction formulas and the ways to calculate the refractive index. Here we will also define Snell’s Law


Refraction Formula

As we know, the refractive index shows how light travels through a medium. So, when light travels from vacuum to a medium, two angles are formed, i.e., angle of incidence(i) and angle of refraction(r), and the formula for refractive index is given by:


n = \[\frac{sin i}{sin r}\]


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 There are two types of refractive index formula, and they are:

  • Absolute Refractive Index

  • Relative Refractive Index


Absolute Refractive Index

The Absolute refractive index is the measurement of light’s speed in any medium compared to the speed of light in a vacuum. So, the Absolute Refractive Index formula:


n = \[\frac{c}{v}\]


Where 

n represents the refractive index,

c represents the speed of light in a vacuum which is 3 X 10⁸ m/s.

And v represents the speed of light in any medium or any other substance.


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Relative Refractive Index

The Relative refractive index is the measurement of light’s speed when it travels from one medium to another. When light travels from a medium with a refractive index (n1) to another medium with a refractive index (n2), we can calculate the refractive index 1n2 by two methods:

  • By dividing the speed of light in medium 1 by the speed of light in medium 2.

  • By dividing the refractive index of medium 2 by the refractive index of medium 2.

So Relative Refractive Index Formula is:


\[_{1}n_{2}\] = \[\frac{C_{1}}{C_{2}}\]


Where, 

₁n₂ represents the relative refractive index,

c₁ represents the speed of light in medium 1,

c₂ represents the speed of light in medium 2.

OR


\[_{1}n_{2}\] = \[\frac{n_{2}}{n_{1}}\]


Where,

₁n₂ denotes the relative refractive index,

n₂ denotes the refractive index of medium 2,

And n₁ represents the refractive index of medium 1.


Snell’s Law of Refraction

This is another formula for the refractive index, which was given by Willebrord Snell, and is known as Snell’s Law. Now how to define Snell’s law.


Snell’s law of refraction states that the ratio of the sine of the angle of incidence and sine of the angle of refraction is constant for a given colour of light. And it is denoted by:


\[\frac{sin i}{sin r}\] = \[\mu\]


Some numerical questions from the refractive index for the students to practice


Here, our certain numerical questions can help students practice numerical questions which can appear in their exams. This will make students more confident while attempting questions during their examination.


Question 1:

Calculate the angle of incidence if the ray is refracted at an angle of 14 degrees and the refractive index of the medium is 1.2.


Solution 1: 

According to the question, the angle of refraction of the ray is 14 degrees and the refractive index of the media is 1.2, therefore, by using Snell’s formula, the ratio of sin I to sin r will be equal to 1.2. 


\[\frac{sin i}{sin r}\] = constant ( \[\mu\] )


\[\frac{sin i}{sin 14}\] = 1.2


\[\frac{sin i}{0.24}\] = 1.2


Sin i = 1.2 * 0.24 = 0.288


i = sin⁻¹0.288 = 16.7 degrees.


Question 2:

Calculate the refractive index of the media if the angle of incidence is 25 degrees and the angle of refraction is 32 degrees.


Solution 2: 

According to the question, the angle of incidence is 25 degrees and the angle of refraction is 32 degrees. Therefore, on applying Snell’s law, the ratio of the sin of the angle of incidence to the sin of the angle of refraction is equal to a constant (refractive index). Thus, the ratio of sin 25 to sin 32 will give the value of the refractive index.


 \[\frac{sin i}{sin r}\] = constant ( \[\mu\] )


\[\frac{sin25}{sin32}\] = \[\frac{0.4226}{0.5299}\] = 0.7975 =0.8


Question 3:

Calculate the refractive index of the medium when the angle of incidence of the ray of light is 30 degrees and the angle of refraction is equal to 50 degrees.


Solution 3:

According to the question, the angle of incidence is 30 degrees and the angle of refraction is 50 degrees. Therefore, the refractive index of the medium is the ratio of the sin of 30 to the sin of 50. 


\[\frac{sin i}{sin r}\] = constant ( \[\mu\] )


\[\frac{sin30}{sin50}\] = \[\frac{0.5}{0.766}\] = 0.6527


Conclusion

Here we studied in detail the refractive index and the ways to calculate it. In short, it’s the measurement of the speed of light as it travels through one medium to another medium and is denoted by n = c/v.

FAQs on Refractive Index Formula

1. Define Snell’s Law.

Snell’s law of refraction states that “The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for the light of a given colour and a given pair of media.” As per the snell’s law definition, the refractive index is:

\[\frac{sin i}{sin r}\] = \[\mu\] 


Where μ denotes constant.


Snell’s Law is a widely used law in the field of optics for the manufacturing of optical apparatus such as eyeglasses and contact lenses. Snell’s law is also used for the measuring of the refractive index of different liquids by the use of the refractometer.

2. State Some of the Applications of Snell’s Law.

According to Snell’s law, the ratio of the sine of the angle of incidence to the sine of the angle of refraction remains the same for the light of a given colour passing through a specific pair of media, that is, sin i/sin r is equal to constant. Snell’s Law is used widely in the field of optics. It’s used to manufacture many optical apparatus such as eyeglasses and contact lenses. Snell’s law is used in the refractometer, to measure the refractive index of different liquids.

3. Light Travels Faster in Water than in Glass. Justify.

The speed of light in any medium is dependent upon the refractive index of the medium in which it is travelling. The speed of light is more in the medium which has a lesser refractive index as compared to the refractive index of the other media. The refractive index of the glass is 1.5 and that of the water is 1.3. Light travels faster in water as the refractive index of water is less than that of glass. The refractive index of water is 1.3 which is less than glass.

4. How is the phenomenon of dispersion related to the refractive index of the material?

When the refractive index of the material increases, the extent to which the light beam is refracted on entering the medium also increases, that is, when a light beam enters from a medium of low refractive index to a medium of high refractive index, then the light beam is refracted with a greater extent. The refractive index of the medium depends upon the frequency of light passing through it. Also, each wavelength of light experiences a slightly different degree of refraction. 


This generally happens when a light beam having different wavelengths of light enters the medium or leaves the medium. The phenomenon of different wavelengths of light being refracted by different degrees is termed dispersion and it is responsible for chromatic aberrations in the objective lens of a microscope.

5. What principle forms the basis of Snell’s law?

The Snell’s law that states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to a constant value, was actually derived from Fermat’s principle. According to Fermat’s principle light travels in the path that is shortest and takes the shortest path. Therefore, Fermat’s principle is also known as the principle of least time and it forms a link between the field of ray optics and wave optics.

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