# Q & A: Reflection and Refraction

Q:
Is there any way that we can explain the refraction and reflection in a single equation?
- Harish Kumar.A (age 15)
Kasaragod,Kerala,India
A:

Good question Harish.

Reflection and refraction are governed by the same basic principle: that a light wave that is reflected and refracted off of a surface remains smooth and continuous.  Reflection and refraction are, as you thought, part of the same process. How much light gets refracted and how much gets reflected are connected - the sum of those adds up to the amount of light that comes in.

Light is a wave of electric and magnetic fields. There are conditions on how the electric and magnetic fields on the two sides of the boundary relate to each other, and in the only way to meet those conditions is to have just the right balance for refracted and reflected light. To write all the conditions in a single equation would require a fancier type of equation than you were probably thinking about. Often, the conditions are written as four equations, describing two parts of both the electric and magnetic fields, one part at right angles to the surface and the other part along the surface plane. These equations are derived from Maxwell's equations.

To solve a reflection/refraction problem in its most general case, you must use the equations that describe the wave that is incident on the surface, and then apply boundary condition equations on the surface. Without the use of these multiple equations and conditions,  as well as Maxwell's equations, we would be very hard pressed to fully describe reflection and refraction. The boundary conditions vary between certain materials though, like if the light is being reflected off of a conductor things will be a bit different.

Samson

(published on 02/23/2013)