Critical Angle Calculator
Calculate the critical angle for total internal reflection in optics with this precise student-and-professional calculator.
Refraction inputs
Enter the refractive indices for medium 1 (optic denser near incident beam) and medium 2 (less dense). Medium 1 must be greater to trigger total internal reflection.
How to Use This Calculator
Provide the refractive indices for the incident medium (n₁) and the transmission medium (n₂). The calculator assumes the beam starts in the optically denser medium (n₁ > n₂). Click Calculate to determine the critical angle, which defines the minimum incident angle that yields total internal reflection.
Methodology
We compute the critical angle via Snell's Law. When light travels from a denser medium into a rarer one, total internal reflection occurs for incident angles greater than θc, where:
θc = arcsin(n₂ / n₁)
The calculator rounds the final angle to two decimal places for consistency.
Glossary of Variables
- n₁ (Medium 1): The refractive index of the incident medium (must be larger).
- n₂ (Medium 2): The refractive index of the medium the light would enter.
- Critical Angle (θc): The incident angle beyond which light cannot exit the first medium.
Step-by-step example
For a glass-air interface with n₁ ≈ 1.50 and n₂ ≈ 1.00, the calculator returns θc ≈ 41.81°. Light hitting the interface at a higher angle reflects entirely back into the glass.
Frequently Asked Questions
What is a critical angle?
The critical angle is the smallest incident angle for which total internal reflection occurs when light tries to leave an optically denser medium.
How do I know if total internal reflection is possible?
It is only possible when n₁ > n₂. Otherwise the calculator returns “N/A” since the sine of the critical angle would exceed 1.
Why use this calculator?
It provides a fast, deterministic way to check critical angles for optics homework, fiber design, or lab planning.
Can the critical angle reach 90 degrees?
No. The value is always below 90° and approaches it only when n₂ is very close to n₁.
Is the output exact?
The calculator uses double precision math and rounds to two decimals. For sensitive setups, cross-check with precise instrumentation.