Refractive index

Imagine what will happen when you are told to run in the pool of water or jam. You will feel difficulty in moving in such a medium or you may run with very low speed. But you can run in the air easily. This is because the water is dense in comparison to the air. Similarly, consider the case of light rays. The light rays can travel in vacuum or air with higher speed but when it travels in mediums like water and glass its speed gets reduced. It is due to the optical density of the medium. The optical density of a material is measured by the refractive index of the medium. Point to note is that optical density and mass density are completely different characteristics of a material though. Let's understand what the refractive index is !

Table of content

• What is the refractive index?
• Absolute refractive index
• Relative refractive index
• Snell’s law
• Practice problem
• FAQs

What is the refractive index?

The optical density of the medium defines the speed of light in that medium. How quickly light moves through a substance depends on its optical density. The refractive index is one such measure of optical density of the medium.

The refractive index or index of refraction of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. It is generally represented by letter n.

Hence,

$n=\frac{Speed of light in vacuum}{Speed of light in medium}$

If the speed of light in the vacuum is c and the speed of light in the given medium is v, then

$n=\frac{c}{v}$

For example:

1. The speed of light in vacuum $c=3\times {10}^8\frac{m}{s}$ hence, the refractive index of the vacuum is $n=\frac{c}{c}=1$.

2. The speed of light in water is $v=2.25\times {10}^8\frac{m}{s}$ hence the refractive index of the water is $n=\frac{3\times {10}^8 }{2.25\times {10}^8}=1.33$

Refractive index of few important material is given below :

In other words, the refractive index measures how much a light beam bends at the interface when it passes through one medium then incident at an angle at the interface and then passes into another. It is determined by Snell's law.

Absolute refractive index

The refractive index is determined using two distinct mediums. However, when one of the two media is regarded as a vacuum, the refractive index of the second medium with respect to the first medium (i.e., vacuum) is referred to as the absolute refractive index. Absolute refractive index is represented by the sign n.

All the refractive index discussed above is absolute refractive index. Hence the absolute refractive index is given as,

$n=\frac{c}{v}$

Where c being the speed of light in a vacuum and v is the speed of light in the medium.

Relative refractive index

The ratio of refractive index of one material to the refractive index of reference material is termed as relative reference index. If a light ray is changing its medium from a medium of refractive index n1 to the medium of refractive index n2 then the refractive index of second medium with respect to the first medium is represented by the n₂₁

$n_{21}=\frac{n_2}{n_1}$

If the speed of light in medium 1 is v₁ and in medium 2 is v₂ then we have,

$n_{21}=\frac{\frac{c}{v_2}}{\frac{c}{v_1}}$

$n_{21}=\frac{v_1}{v_2}$

Hence the relative refractive index of medium 2 with respect to the merium 1 is equal to the ratio speeds in medium 1 to that of in medium 2.

Snell’s law

When a light ray changes its medium of travel, then it deviates from its path (when incident at an angle on the interface). This deviation can be descrbed by the snell’s law.

Suppose a light ray is travelling in medium 1 of refractive index n1, incident at an angle of i. When it refracts into a medium of refractive index n2 at an angle r. Then, according to Snell's law the ratio of the sine of the angle of incidence, i to the sine of the angle of refraction, r is equal to the refractive index of medium 2 w.r.t. Medium 1.

$\frac{\mathit{S}\mathit{i}\mathit{n}\mathit{ }\mathit{i}}{\mathit{S}\mathit{i}\mathit{n}\mathit{ }\mathit{r}}=\frac{{\mathit{v}}_1}{{\mathit{v}}_2}=\frac{{\mathit{n}}_2}{{\mathit{n}}_1}$

or, $n_1\times \sin i=n_2\times \sin r$

This is the expression for snell's law.

Practice problems

Q1. Light travels at a speed of $3\times {10}^8\frac{m}{s}$ in air and $2\times {10}^8\frac{m}{s}$ in glass. The glass's refractive index is?

Answer. Given $c=3\times {10}^8\frac{m}{s}$

$v=2\times {10}^8\frac{m}{s}$

The refractive index of the glass is, $n_{ga}=\frac{c}{v}$

$n=\frac{3\times {10}^8\frac{m}{s}}{2\times {10}^8\frac{m}{s}}$

n=1.5

Hence the refractive index of the glass is 1.5

This is actually the refractive index of glass with respect to air. The refractive index of air is considered to be 1

Q2. The diamond has a refractive index of 2.41. How fast does light move in a diamond?

Answer:  Given n=2.41

Also we the speed of light in the vacuum is $c=3\times {10}^8\frac{m}{s}$

The refractive index of the material is given by, $n=\frac{c}{v}$

$v=\frac{c}{n}$

$v=\frac{3\times {10}^8}{2.41}$

$v\approx 1.245\times {10}^8\frac{m}{s}$

Hence the speed of the light in the diamond is $1.245\times {10}^8\frac{m}{s}$

Q3. Glass has a refractive index of 1.5 while water has a refractive index of 1.33. What is the glass's refractive index if it is placed in water?

Answer. Given n_glass=1.5 and n_water=1.33

As glass is placed inside the water, the refractive index of the glass with respect to water is to be calculated.

$n_{glass , water}=\frac{n_{glass}}{n_{water}}$

$n_{glass , water}=\frac{1.5}{1.33}$

$n_{glass , water}\approx 1.128$

Hence the refractive index of the glass with respect to water is 1.128

Q4. A light ray incident at a water-glass interface at an angle of incidence 30^o. If the refractive index of glass is 1.5 and that of water is 1.33, find the angle of refraction.

Answer: Given i=30^o

n_w=1.33 and n_g=1.5

From question it is clear that the light ray is travelling from the water to the glass.

Using the snell’s law,

$n_w\times \sin i=n_g\times \sin r$

$1.33\times \sin {30}^o=1.5\times \sin r$

$Sin r =\frac{ 1.33}{1.5}\times Sin {30}^o$

r=26.31^o

Angle of refraction in the glass is 26.31^o.

FAQs

Q1. What is the unit of refractive index ?
Answer:  The refractive index is a ratio of speeds in different mediums. And we know that the ratio of similar quantities has no unit. So, the refractive index is a unit less quantity.

Q2. What factors affect the refractive index?
Answer: Refractive index is affected by the two factors:

1. temperature of the medium: Generally, the refractive index is measured at standard temperatures. Usually, with the increase in temperature, the refractive index of the medium decreases.

2. wavelength of the light: The reference index is inversely proportional to the wavelength of the light.

Q3. What is the significance of refractive index in the refraction of light?
Answer: The refractive index is a measurement of how much a light beam bends as it passes through various materials. The ratio of a light ray's speed in an empty space (i.e., vacuum) to its speed inside a substance is a way to define the refractive index of the substance.

Q4. Can the value of the refractive index be less than one?
Answer: Since the speed of light in any media is always lower than the speed in vacuum, the refractive index of a material is always more than 1.

The refractive index of the material is given by $n=\frac{c}{v}$

Where, c is the speed of light in a vacuum and v is the speed of light in the medium.

Hence it cannot be less than 1.