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Critical Angle Calculator

Work out critical angle instantly with clear inputs, formula shown and shareable results.

About Critical Angle Calculator

The critical angle is where the refracted ray would graze the boundary at 90 degrees, so sin(theta c) = n2/n1. Glass to air at 1.5 and 1.0 gives 41.8 degrees - which is why a 45 degree prism reflects totally without any coating. No critical angle exists when the second medium is denser.

Formulas

Critical angle

sin(theta c) = n2 / n1, requires n1 > n2

Beyond it

all light is reflected internally

Worked example

With the default values below, Critical Angle Calculator returns Critical Angle of 41.810. Change any input above and every figure here is recalculated in your browser.

Inputs used

Refractive index of the denser mediumminimum 0
1.5
Refractive index of the lighter mediumminimum 0
1

Results

Critical Angle
41.810 deg
Index Ratio n2/n1
0.6667
Interpretation
Total internal reflection occurs beyond this angle
Grazing Angle Equivalent
48.190 deg

Step by step

  1. 1Values used
  2. 2Critical angle
  3. 3Beyond it
  4. 4Critical Angle= 41.810 deg
  5. 5Index Ratio n2/n1= 0.6667
  6. 6Interpretation= Total internal reflection occurs beyond this angle
  7. 7Grazing Angle Equivalent= 48.190 deg

Assumptions and limits

  • The result is derived only from the 2 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 4 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 is water's critical angle to air?

About 48.6 degrees for n = 1.333, which produces Snell's window - the circular view of the sky seen from underwater.

Why do optical fibres rely on this?

Because light striking the core-cladding boundary beyond the critical angle is reflected with essentially no loss, guiding it for kilometres.

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