Table of Contents

## 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.