Refractive Index - Formula & Example - Vedantu

Refractive index is a measure of the bending of a ray of light when it passes from one medium into another. When light travels from air into glass or water, its speed changes, which causes the light to bend at the interface between the two materials. The degree to which this bending occurs depends on the refractive indices of both media.

Definition and Concept

The refractive index of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium. It quantifies how much the path of light bends or refracts when entering the material from another medium, typically from air or vacuum.

A higher refractive index means that light slows down more and bends more sharply when entering the new material.

Refractive Index Formula

The basic relationship can be expressed mathematically as:

n = c / v

Where:

n = refractive index of the medium c = speed of light in vacuum v = speed of light in the medium

Since both the numerator and denominator are speeds (units: m/s), the refractive index is a dimensionless quantity.

Key Data Table: Refractive Index Values

Medium	Refractive Index (n)
Vacuum	1.00
Air	1.0003
Water	1.33
Crown Glass	1.52
Diamond	2.42

Explanation with Example

Consider a ray of light passing from air into water. Because water has a higher refractive index than air, the light slows down and bends towards the normal (an imaginary line perpendicular to the interface). This bending can be observed, for example, when looking at a straw placed in a glass of water—the straw appears bent at the water's surface.

Example Calculation: Suppose the speed of light in a medium is 2 x 108 m/s. The speed of light in vacuum (c) is approximately 3 x 108 m/s. The refractive index n is:

n = c / v = (3 x 108) / (2 x 108) = 1.5

This means light travels 1.5 times slower in the given medium compared to vacuum.

Step-by-Step Approach for Problem Solving

• Write the basic formula: n = c / v.
• Determine and substitute the correct values for the speed of light in vacuum (c) and the medium (v).
• Calculate the value of the refractive index.
• Interpret the physical significance. If n > 1, the medium is optically denser than vacuum.

Key Formulas and Applications

Formula	Description
n = c / v	Refractive index in terms of speed of light
n1 sinθ1 = n2 sinθ2	Snell's Law (relates the refractive indices and angles in two media)

Practical Relevance of Refractive Index

• Refraction: Understanding how lenses focus light relies on refractive index.
• Lenses: The power and magnification depend on the refractive indices of materials.
• Total internal reflection, critical angle: Occurs when light cannot exit a medium but reflects entirely inside.
• Optical fibers: Use the refractive index difference for signal transmission.

Summary Table: Key Points

Concept	Description
Refractive Index (n)	Ratio of light speed in vacuum to in medium; dimensionless
Physical Meaning	Indicates how much light bends when entering a material
Application	Explains bending of light, lens behavior, and optical phenomena

Practice and Further Learning

• Practice calculating refractive index values from given speeds using n = c / v.
• Explore more about refractive index and refraction of light for additional examples.
• Connect the refractive index concept with concave and convex lenses for practical optics.
• Move forward to topics like dispersion of light and reflection for advanced problems.