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

(Image will be Uploaded Soon)

 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.

(Image will be Uploaded Soon)

(Image will be Uploaded Soon)

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.