Refractive Index Formula 

What is the Refractive index of a medium?

• Light bends while traveling from one medium to another due to a change in its speed. This is known as the refraction of light.
• When a ray of light travels from an optically denser medium to an optically rarer medium, its speed increases, and the ray of light moves away from the normal.
• When a ray of light travels from an optically rarer medium to an optically denser
  medium, its speed decreases, and the ray of light moves toward the normal.
• The Refractive index of a refractive medium with respect to an incident medium is defined as the ratio of the speed of light in an incident medium to the speed of light in a refractive medium.

For example, if medium 1 is the incident medium and medium 2 is the refractive medium, then the refractive index of medium 2 with respect to medium 1 is denoted by n21.

It is given by:

• When the refractive index of medium 2 with respect to medium 1 is greater than 1, it means that the speed of light in medium 2 is less than that in medium 1. Thus, the light will bend towards the normal.
• When the refractive index of medium 2 with respect to medium 1 is lesser than 1, it means that the speed of light in medium 1 is less than that in medium 2. Thus, the light will bend away from the normal.
• The ratio of the speed of light in a vacuum to that in any medium is the refractive index of the medium with respect to the vacuum, also known as the absolute refractive index. It is represented by medium

The absolute refractive indices of some materials are as follows

Medium material	Absolute refractive index
Air	1.0003
Canada balsam	1.53
Ice	1.31
Water	1.33
Rock salt	1.54
Alcohol	1.36
Kerosene	1.44
Carbon disulphate	1.63
Fused quartz	1.46
Turpentine oil	1.47
Benzene	1.50
Crown glass	1.52
Diamond	2.42
Dense flint glass	1.65

Solved Examples on Refractive Index formula

Example 1: A light ray passes from air into a medium with a refractive index of 1.5. Calculate the angle of refraction if the angle of incidence is 30 degrees.

Solution:

Given:

Refractive index of the medium (n) = 1.5

Angle of incidence (i) = 30 degrees

Using Snell’s Law, the relationship between the angles of incidence and refraction can be expressed as:

n1 x sin(i) = n2 x sin(r)

Since the light is passing from air (with a refractive index of approximately 1) to the medium, the equation simplifies to:

1 x sin(30) = 1.5 x sin(r)

sin(r) = (1 x sin(30)) / 1.5

sin(r) = 0.5

To find the angle of refraction, we take the inverse sine sin-1 of 0.5:

r = sin-10.5

r ≈ 30 degrees

Therefore, the angle of refraction is approximately 30 degrees.

Example 2: A light ray travels from water (refractive index = 1.33) into a medium with an unknown refractive index. If the angle of incidence is 45 degrees and the angle of refraction is 30 degrees, calculate the refractive index of the unknown medium.

Solution:

Given:

Refractive index of water (n1) = 1.33

Angle of incidence (i) = 45 degrees

Angle of refraction (r) = 30 degrees

Using Snell’s Law:

n1 x sin(i) = n2 x sin(r)

Plugging in the values:

1.33 x sin(45) = n2 x sin(30)

n2 = (1.33 x sin(45)) / sin(30)

n2 ≈ 1.92

Therefore, the refractive index of the unknown medium is approximately 1.92.

Frequently Asked Questions on Refractive Index Formula

What is the refractive index?

The refractive index is a dimensionless quantity that measures how much a material can change the speed of light as it passes through it. It is the ratio of the speed of light in a vacuum to the speed of light in the material.

What is the formula for refractive index?

The formula for refractive index (n) is given by: n = c / v Where: n is the refractive index, c is the speed of light in a vacuum (approximately 3.00 × 108 meters per second), v is the speed of light in the medium.

What does a higher refractive index indicate?

A higher refractive index indicates that light travels slower in the medium. It means that the medium has a stronger ability to bend or refract light compared to a medium with a lower refractive index.

How does refractive index affect the direction of light?

When light passes from one medium to another with a different refractive index, it changes its direction. This phenomenon is called refraction. The amount and direction of the change in direction depend on the refractive indices of the two media.

What factors can affect the refractive index of a material?

The refractive index of a material can be affected by factors such as temperature, pressure, and the wavelength of light. In some materials, the refractive index can also depend on the polarization of the light.