Critical angle calculator

Calculate critical angle with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use critical angle to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Incident refractive index
1.5
Transmitted refractive index
1
Critical angle (degrees, or no critical angle)
41.810315

Try another scenario

Incident refractive index
1.6500000000000001
Transmitted refractive index
1
Critical angle (degrees, or no critical angle)
37.305201
Calculation method

Calculation method

Critical angle (degrees, or no critical angle)

Critical angle=asin(n2/n1) only when n1>n2.

Symbols and units
a
Incident refractive index
b
Transmitted refractive index

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Calculation uses the entered values and stated mathematical model; quantities must use the labelled units. Supported limits: All required fields must be finite values of the exact declared type and within displayed bounds. Lists contain1–1000 finite numbers. JSON tables are numeric rectangular rows, at most100 rows and30 columns; individual tools have stricter shape/domain constraints. Critical angle=asin(n2/n1) only when n1>n2.
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