Critical Angle Calculator Formula

Understand the math behind the critical angle calculator. Each variable explained with a worked example.

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Formulas Used

Critical Angle

critical_angle = asin(n2 / n1) * 180 / pi

Variables

VariableDescriptionDefault
n1Denser Medium Refractive Index1.5
n2Less Dense Medium Refractive Index1

How It Works

Critical Angle

The critical angle is the angle of incidence above which total internal reflection occurs when light travels from a denser to a less dense medium.

Formula

theta_c = arcsin(n2 / n1)

where n1 > n2. Above this angle, no light passes through the boundary.

Worked Example

Light going from glass (n=1.5) to air (n=1).

n1 = 1.5n2 = 1
  1. 01theta_c = arcsin(n2/n1)
  2. 02theta_c = arcsin(1/1.5)
  3. 03theta_c = arcsin(0.667)
  4. 04theta_c = 41.81°

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