Reflection and Refraction

Consider a light ray which encounters a surface separating two regions with different indices of refraction, as shown below.

The reflected and transmitted ray directions are given by the law of reflection:

q_i = q_t

and the law of refraction (Snells law):

n_isin(q_i) = n_tsin(q_t)

where q_i and q_t are defined in the figure above, and n_i and n_t are the indices of refraction in the incident and transmitted regions. The index of refraction is defined by

where c is the speed of light in vacuum, and v is the speed of light in the region.

Note that since the velocity decreases when the region is not a vacuum, the product fl must also decrease. It is interesting that the frequency remains unchanged (frequency determines color); it is the wavelength that changes:

where l₀ is the vacuum wavelength and l_n is the wavelength in the medium with index of refraction n.