Total internal reflection

Also called TIR

The complete reflection of light back into a medium when it strikes the boundary with a lower-index medium at an angle of incidence beyond the critical angle. No light at all is transmitted across the boundary.

Two conditions, and both are required.

  1. The light must be travelling from a higher index medium toward a lower index one. Going the other way, there is no critical angle and no total internal reflection, ever.
  2. The angle of incidence, measured from the normal, must exceed the critical angle.
θc=arcsin⁡ ⁣(n2n1)\theta_c = \arcsin\!\left(\frac{n_2}{n_1}\right)

The CED labels that a derived equation, which by its own definition means it is not printed on the exam equation sheet. Produce it from Snell's law instead: set θ2=90\theta_2 = 90 degrees, so n1sin⁡θc=n2sin⁡90∘=n2n_1 \sin\theta_c = n_2 \sin 90^\circ = n_2.

At exactly the critical angle the refracted ray grazes along the surface at 90 degrees to the normal. Past it, the CED says all light is reflected and none is transmitted into the other medium. Note that ordinary partial reflection happens at every angle; what the critical angle changes is that the transmitted part disappears.

Numbers worth carrying: water to air gives θc=arcsin⁡(1/1.33)\theta_c = \arcsin(1/1.33), about 49 degrees, and glass of index 1.5 to air gives about 42 degrees. That 42 is why a 45 degree prism turns a beam through a right angle with no silvering, and why an optical fibre keeps light inside a bend.

The angle depends only on the ratio of the two indices, so the closer they are, the larger θc\theta_c becomes. Topic 13.3 has the CED statements.

Back to the physics glossary