When to use this calculator
Find the incidence angle at which ideal total internal reflection begins. Requires propagation from the higher-index medium toward a lower-index medium.
Explore the optics & quantum relationships calculators for other questions in this topic. For a related calculation, use the De Broglie Wavelength Calculator: Find the matter-wave wavelength corresponding to a momentum magnitude.
PUTTING IT INTO PRACTICE
Critical Angle: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Higher refractive index | 2 |
| Lower refractive index | 1 |
| Result | 30 degrees |
- Check the input labels and enter the example values above.
- Apply the relationship: Critical angle = asin(lower index/higher index).
- The result is 30 degrees, rounded for display.
How to interpret your result
Requires propagation from the higher-index medium toward a lower-index medium.
Use the stated sign convention for lenses and angles measured to the normal for refraction. Vacuum wavelength differs from wavelength inside a material. These models do not account for every optical aberration or material response.
Frequently asked questions
Why can a refracted-angle calculation have no real result?
When Snell’s-law sine exceeds one, the ideal ray model predicts total internal reflection rather than a real transmitted angle.
When is the critical angle calculator useful?
Find the incidence angle at which ideal total internal reflection begins. Requires propagation from the higher-index medium toward a lower-index medium.
How do I use the critical angle calculator?
Enter higher refractive index, lower refractive index. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Critical angle = asin(lower index/higher index).
What should I check before using the result?
Requires propagation from the higher-index medium toward a lower-index medium.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Calculators Map editorial process · Updated · Methods and limitations