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Total Internal Reflection Calculator

Work out total internal reflection instantly with clear inputs, formula shown and shareable results.

About Total Internal Reflection Calculator

Snell's law, n1 sin(theta1) = n2 sin(theta2), decides the outcome at a boundary. Air into glass at 30 degrees refracts to 19.47 degrees, bending towards the normal. Going the other way, if the required sine exceeds one there is no solution and the light is totally internally reflected instead.

Formulas

Snell's law

n1 sin(theta1) = n2 sin(theta2)

Total internal reflection

occurs when n1 sin(theta1) / n2 > 1

Worked example

With the default values below, Total Internal Reflection Calculator returns Angle Of Refraction of 19.471. Change any input above and every figure here is recalculated in your browser.

Inputs used

Refractive index of the incident mediumminimum 0
1
Refractive index of the second mediumminimum 0
1.5
Angle of incidenceaccepts 0–90 deg
30 deg

Results

Angle Of Refraction
19.471 deg
Critical Angle For This Pair
90.000 deg
What Happens
Refracts towards the normal - entering a denser medium
Ray Deviation
10.529 deg

Step by step

  1. 1Values used
  2. 2Snell's law
  3. 3Total internal reflection
  4. 4Angle Of Refraction= 19.471 deg
  5. 5Critical Angle For This Pair= 90.000 deg
  6. 6What Happens= Refracts towards the normal - entering a denser medium
  7. 7Ray Deviation= 10.529 deg

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What does Snell's law give for air into glass at 30 degrees?

sin(theta2) = 1.0 x sin(30) / 1.5 = 0.3333, so the refracted ray is at 19.47 degrees.

Can total internal reflection happen going into a denser medium?

Never. The refracted sine is always smaller than the incident one, so a solution always exists.

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