Refractive Index
Ratio of light speed in vacuum to that in a medium.
Formula
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Example
Water ≈ 1.33
How it works
The refractive index tells you how much a material slows light down compared with empty space. Since light travels at its maximum speed in vacuum, the ratio n = c/v measures the reduction in speed caused by the material’s interaction with the electromagnetic wave. A larger n means light travels more slowly in that medium, which is why it bends more when entering it at an angle.
When to use it
Use this formula when you know the speed of light in a material and want to compare it with vacuum, or when you want to find the speed of light in a medium from its refractive index. It is especially useful in optics problems involving refraction, lenses, prisms, and materials like glass, water, or plastic.
Worked example, step by step
A piece of glass has a refractive index of 1.50. What is the speed of light in the glass? Step 1: Write the formula: n = c / v Step 2: Rearrange to find v: v = c / n Step 3: Substitute values: v = 3.00 × 10^8 m/s ÷ 1.50 Step 4: Calculate: v = 2.00 × 10^8 m/s Final answer: light travels at 2.00 × 10^8 m/s in the glass.
Common mistakes to avoid
- Using the speed of light in air instead of vacuum for c, when high precision is needed
- Forgetting to rearrange the formula correctly and dividing the wrong way round
- Confusing refractive index with wave speed itself; n is a ratio, not a speed
Did You Know?
Diamond's very high refractive index traps and bounces light inside it, producing that famous sparkle.
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