Refraction means the bending of a wave resulting from a change in its velocity as its moves from one medium to another. Since the frequency of a wave cannot change, independent of the source changing its frequency when it originally emits a wave, this change in wave velocity must result from a change in its wavelength in the second medium.

 

 

 

As shown in the above diagram, when the waves encounter an oblique interface, both their direction and wavelength change. In the instance illustrated, the wavelengths shorten and the refracted rays "bend towards the normal" as the waves enter the shallow, or slower, medium: θ_r < θ_i.

 

 

This diagram illustrates that when an incident wave crosses an interface and its wavefronts are parallel to the interface, the wave will still exhibit a change in wavelength but there will be no change in direction since its rays are parallel to the normals.

 

Now we will extend our discussion of refraction to light waves. To quantify the degree of refraction, we will introduce a dimensionless quantity called the index of refraction, n.

 

n = c/v

 

In this formula,

 

This defining formula can be easily modified to describe the changes that occur in wavelength during refraction.

 

n = c/v
n = (f λ)/(f λ_n)

n = λ/λ_n

 

Notice that the frequency, f, cancels since it is an invariant and does not depend on the medium through which the wave is traveling.

 

Some common indices of refraction for a midrange wavelength of light (589 nm, a prominent line in the emission spectrum of sodium) are:

 

vacuum	1.00000	fused quartz	1.46
air (STP)	1.00029	crown glass	1.52
water (20ºC)	1.33	polystyrene	1.55
acetone	1.36	carbon disulfide	1.63
ethyl alcohol	1.36	flint glass (heavy)	1.65
sugar solution (30%)	1.38	sapphire	1.77
sugar solution (80%)	1.49	diamond	2.42