Critical Angle Calculator
Finds the incident angle for the onset of total internal reflection. Changing an input shows how the reported quantity responds.
Supply the lens or mirror data
Critical angle
The geometry behind the output
Finds the incident angle for the onset of total internal reflection. The calculation keeps higher refractive index, lower refractive index visible and reports critical angle in deg.
The ray must travel from the higher-index medium toward the lower-index medium for a critical angle to exist.
The critical angle page labels each value before it enters the equation. That prevents an angle convention, temperature scale, optical sign, or reference quantity from becoming an invisible assumption.
Check the image sign and magnitude
Reduce the dimensions in θc = asin(n₂ / n₁) until they agree with deg. For logarithms, trigonometric functions, and ratios, also verify that their arguments are dimensionless and inside the permitted domain.
Change one source value slightly and predict the direction of critical angle first. If the screen moves the other way, revisit the equation, signs, and reference frame.
Following θc = asin(n₂ / n₁)
For critical angle, identify critical angle as the sought quantity and copy the printed relationship before using the sample data. This establishes an auditable direction for the arithmetic.
Keep the sign convention and denominator explicit in θc = asin(n₂ / n₁); a finite answer alone does not prove that the setup is physical.
A numerical example for critical angle
The starting condition is Higher refractive index = 1.5 ratio; Lower refractive index = 1 ratio. It gives a fixed reference result before any input is changed.
After solving for critical angle, rearrange θc = asin(n₂ / n₁) for one entered quantity. Recovering that entry checks a different algebraic direction instead of repeating the same calculation.
Using critical angle beyond this page
Use extra internal precision to reverse-check θc = asin(n₂ / n₁), while the final reported critical angle remains limited by the least certain input.
Record the operating condition, formula, units, and convention beside critical angle. Those details distinguish a physically reproducible answer from a number copied out of context.
Effects excluded from Critical Angle
The critical angle relationship uses paraxial rays or an ideal interference geometry. Thick elements, aberrations, polarization, dispersion, and large angles may require a more complete optical model for critical angle.
Do not hide a violated critical angle assumption inside an unexplained correction factor.
Where the Critical Angle result can lead
From this result, compare refractive index from light speed calculator, thin lens focal length calculator, snell law refraction angle calculator and thin lens image distance calculator.
A repeated field name is not enough; the next equation must describe the same Critical Angle situation.
Common Critical Angle questions
What does critical angle represent?
It is the value of θc = asin(n₂ / n₁) under the units, field meanings, and optics assumptions printed on the critical angle page.
How can critical angle be checked?
Rearrange θc = asin(n₂ / n₁) to recover an entered value, reduce the surviving unit to deg, and compare the scale with the physical setup.
Do the displayed units matter?
Yes. Convert each measurement to the unit beside its field before evaluating the critical angle relationship.
Why might another critical angle differ?
Another medium, temperature, geometry, reference frame, boundary condition, or sign convention can change the reported critical angle.
Can critical angle be negative?
On the critical angle page, a negative value is meaningful only when the printed sign convention and equation permit it; otherwise it signals an invalid domain.
How should the result be rounded?
Keep guard digits while critical angle enters another operation, then report only the precision supported by the least certain source measurement.