When to use this calculator
Find the refracted ray angle at a boundary between optical media. An out-of-range sine indicates total internal reflection rather than a real transmitted ray.
Explore the optics & quantum relationships calculators for other questions in this topic. For a related calculation, use the Thin Lens Image Distance Calculator: Find ideal image distance for a thin lens and a real object.
PUTTING IT INTO PRACTICE
Snells Law: 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 |
|---|---|
| Incident index | 1 |
| Transmitted index | 2 |
| Incident angle to normal (degrees) | 30 |
| Result | 14.477512 degrees |
- Check the input labels and enter the example values above.
- Apply the relationship: Refracted angle = asin(n₁ sin(incident angle)/n₂).
- The result is 14.477512 degrees, rounded for display.
How to interpret your result
An out-of-range sine indicates total internal reflection rather than a real transmitted ray.
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 snells law calculator useful?
Find the refracted ray angle at a boundary between optical media. An out-of-range sine indicates total internal reflection rather than a real transmitted ray.
How do I use the snells law calculator?
Enter incident index, transmitted index, incident angle to normal (degrees). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Refracted angle = asin(n₁ sin(incident angle)/n₂).
What should I check before using the result?
An out-of-range sine indicates total internal reflection rather than a real transmitted ray.
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.
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