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Refractive index calculator

A-level Waves

The refractive index of a material compares the speed of light in a vacuum with the speed in the material.

n = c / v

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

nRefractive index to find 1.50

cSpeed of light constant m/s

vSpeed of light in the material

Significant figures

Working

Write the equation
n = c / v
Constants used
c = 3 × 10⁸ m/s
Substitute the values
n = (3 × 10⁸) ÷ (2 × 10⁸)
Calculate
n = 1.5
Give the answer to 3 significant figures
n = 1.50

Worked example

Find n, the refractive index. Given: speed of light in the material v = 2.00 × 10⁸ m/s; speed of light c = 3 × 10⁸ m/s.

Write the equation
n = c / v
Constants used
c = 3 × 10⁸ m/s
Substitute the values
n = (3 × 10⁸) ÷ (2 × 10⁸)
Calculate
n = 1.5
Give the answer to 3 significant figures
n = 1.50

Symbols and units

Symbol	Quantity	SI unit
n	Refractive index	no unit
c	Speed of light (constant)	m/s
v	Speed of light in the material	m/s

Refractive index: rearranged

To find refractive index: n = c / v
To find speed of light in the material: v = c / n

Exam tip

The speed in the material is always less than c, so n is always greater than 1.

Common questions

What is the formula for refractive index?

The equation is n = c / v, where n is the refractive index; v is the speed of light in the material (m/s); c is the speed of light (m/s).

What units should I use for refractive index?

In SI units: refractive index in no unit (a ratio), speed of light in m/s, speed of light in the material in m/s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange n = c / v?

Rearranging gives these forms: to find refractive index: n = c / v. to find speed of light in the material: v = c / n.

Practise refractive index questions

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Read the full explanation on the Refractive index formula page. More waves equations: Wave speed, Frequency and time period, Magnification, Snell’s law, Critical angle, Double-slit fringe spacing, Diffraction grating, Intensity. See the full list on the a-level physics equation calculator page.