Refractive Index & Snells Law

This lesson covers:

  1. What 'refractive index' means
  2. How to find the refractive index of a material 
  3. How to use the Snell's Law equation

Refractive index


The refractive index of a material is a measure of the speed of light as it passes through that material, compared to the speed of light as it passes through a vacuum.

Materials through which light travels more slowly, for example diamond, have a higher refractive index (e.g. diamond has a refractive index of 2.4).

 Materials through which light travels more quickly, for example water, have a lower refractive index (e.g. ice has a refractive index of 1.3.

The medium with the lowest refractive index is a vacuum, as light travels fastest in a vacuum.


A vacuum has a refractive index of 1.

Will the refractive index of glass be higher or lower than 1?

Higher 

Lower

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Ice has a refractive index of 1.3, while sapphire has a refractive index of 1.8. 


Which medium will light travel fastest through, ice or sapphire?

Ice

Sapphire

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How to find the refractive index of a material


To find the refractive index of a material we can use the equation below, where n is the refractive index, c is the speed of light in a vacuum, and v is the speed of light in that material.


refractive index = speed of light in materialspeed of light in vacuum


it can also be written as:


n=vc

The formula for the refractive index is:

n=c×v
n=cv
n=v×c
n=vc

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Refractive index - worked example:


'Light travels at 3 x 108 m/s in a vacuum and 1.24 x 108 m/s in diamond

Calculate the refractive index of diamond.'


The refractive index of water is 1.33. The speed of light in a vacuum is 3.00 x 108m/s.

What is the speed of light in water?

3.14 x 10m/s

2.26 x 108 m/s

1.56 x 10m/s

2.58 x 10m/s

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The speed of light in Perspex is 1.99 x 108 m/s, while the speed of light in a vacuum is 3.00 x 108 m/s.


What is the refractive index of Perspex? Give your answer to 2 d.p.

1.51

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Snell's law

Diagram illustrating Snell's law with incident ray, refracted ray, angle of incidence, and angle of refraction.

Snell's law is an equation that links the refractive index (n), the angle of incidence (i), and angle of refraction (r).


The formula for Snell's law is:

n=sin(r)sin(i)

Snell's law - worked example


A ray of light travels from air into glass. 

The angle of incidence is 28°, and the angle of refraction is 18°


Calculate the refractive index of the glass.

A ray of light enters a beaker of acetone with an angle of incidence of 35°. The ray is refracted with an angle of refraction of 25°.


What is the refractive index of acetone? Give your answer to 2 d.p.

1.36

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A ray of light enters a pane of glass with an angle of incidence of 40°. The refractive index of the glass is 1.5. 


What will the angle of refraction be? Give your answer to the nearest degree.

25

°

°

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Snell's Law is:

n=sinrsini
n=sinisinr
n=sinr×sini

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