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Refractive Index Formula

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What is the Refractive Index Formula?

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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 formula 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 in a vacuum, 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 = \[\frac{\text{sin i}}{\text{sin r}}\]

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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:

1n2 = \[\frac{c_{1}}{c_{2}}\]

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

1n2 = \[\frac{n_{2}}{n_{1}}\]

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:

\[\frac{\text{sin i}}{\text{sin r}}\] = μ


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.

FAQ (Frequently Asked Questions)

Q1. Define Snell’s Law.

Ans. 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, refractive index is: 

sin i/sin r = μ

Where μ denotes constant.

Q2. State Some of the Applications of Snell’s Law.

Ans. 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.

Q3. Light Travels Faster in Water than in Glass. Justify.

Ans. 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.