Critical Angle

\sin\theta_c = \frac{n_2}{n_1}

The angle of incidence above which total internal reflection occurs (when going from denser to less dense medium).

Variables

θ_c

Critical angle

n₁

Refractive index of denser medium

Allowed values: 1 or more

unitless

n₂

Refractive index of less dense medium

Allowed values: 1 or more

unitless

Your notes

0/5000

Check value

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n₁ = 2.5 (Refractive index of denser medium)
n₂ = 1.5 (Refractive index of less dense medium)

Result: θ_c = 36.869898 °

Where this formula is listed

Optics formulas, under Refraction, alongside Refractive Index and Apparent Depth.
In the optics list it comes after Refractive Index and before Apparent Depth.
Optics formula sheet, one of 34 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Critical Angle formula?

Critical Angle is written sin θ_c = n₂/n₁. The angle of incidence above which total internal reflection occurs (when going from denser to less dense medium). It belongs to Optics, under Refraction.

What are the units in sin θ_c = n₂/n₁?

In SI units, θ_c is critical angle, measured in °; n₁ is refractive index of denser medium (dimensionless); n₂ is refractive index of less dense medium (dimensionless).