Data Source and Methodology
All calculations are based strictly on the principles of Snell's Law and the critical angle formula derived from it. For more detailed information, refer to standard physics textbooks.
The Formula Explained
\( \text{Critical Angle} = \arcsin\left(\frac{n_2}{n_1}\right) \)
Glossary of Variables
- Refractive Index of Medium 1 (\( n_1 \)): The refractive index of the initial medium.
- Refractive Index of Medium 2 (\( n_2 \)): The refractive index of the second medium.
- Critical Angle: The angle above which total internal reflection occurs.
How It Works: A Step-by-Step Example
Let's consider a glass-air interface, where \( n_1 \) (glass) is 1.5 and \( n_2 \) (air) is 1.0. Using the formula, the critical angle is calculated as follows:
\( \text{Critical Angle} = \arcsin\left(\frac{1.0}{1.5}\right) \approx 41.8^\circ \)
Frequently Asked Questions (FAQ)
What is a critical angle?
The critical angle is the angle of incidence above which light is completely reflected inside a medium rather than passing through the boundary.
How do I use this calculator?
Enter the refractive indices of the two media. The calculator will determine the critical angle for total internal reflection.
Why is the critical angle important?
Understanding the critical angle is crucial for designing optical devices and understanding light behavior in different media.
Can the critical angle be greater than 90 degrees?
No, the critical angle is always less than or equal to 90 degrees.
What happens if the refractive index of medium 2 is greater than medium 1?
If \( n_2 > n_1 \), total internal reflection cannot occur, and thus no critical angle exists.
Formula (LaTeX) + variables + units
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\( \text{Critical Angle} = \arcsin\left(\frac{n_2}{n_1}\right) \)
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Last code update: 2026-01-19
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