# Q & A: Total Internal Reflection

Q:
What do they mean by total internal reflection? And how does this take place?
- Anonymous (age 15)
Singapore
A:

Total internal reflection is when the light inside some material (like glass) is all reflected when it hits a surface. Snell's Law, n1*sin(Θ1)= n2*sin(Θ2) describes refraction (bending) of light at a boundary between two materials. The stuff on the right hand side of the equation is for the incoming light ( n1 is the index of refraction and Θ1 is the angle the ray of light makes with the "normal", an imaginary line drawn perpendicular to the boundary). The left hand side is the index of refraction and the angle for the refracted ray of light. The index of refraction is different for each material and is the found by using n = c/v , where c is the speed of light in a vacuum (3.0 *108 m/s) and v is the speed of light in some material. When light passes from a material with a higher index of refraction to one with a lower index of refraction, there is a specific angle for incoming light which will give an angle of refraction of 90°. The specific angle is called the critical angle(Θc). All of the light is reflected when

n1*sin(Θc) = n2*sin(90°),

which is the same as saying sin(Θc) = n2/n1

or Θc = arcsin(n2/n1)

So when Θ1 is equal to or greater than Θc, all of the light is "stuck" inside the material.

See this image: for a picture of how the transmitted refracted ray and the reflected ray go. For close grazing, there is no transmitted ray.

(published on 10/22/2007)