Calculating critical angles

What you will learn

Use sin C = 1/n for a glass–air boundary.

Specification mapping: A2.1.3

Prerequisites: A2.1.2

Physical principles

At the critical angle, Snell’s law gives n₁ sin C = n₂ sin 90°. Therefore sin C = n₂/n₁. For glass to air with air index approximately one, this reduces to sin C = 1/n. The critical angle is C = sin⁻¹(1/n), not 1/sin n.

A higher glass index gives a smaller glass–air critical angle. Check the ratio is between zero and one before taking inverse sine. For a core–cladding boundary, use the ratio of cladding to core index instead of the air expression. All indices must refer to the same wavelength and conditions.

A calculated C sets the boundary between refraction and TIR, not a ray angle to the fibre axis. Use the normal to the local surface when comparing the incidence angle. In a cylindrical fibre, this geometric distinction matters when drawing zigzag paths.

Scientific diagram and interpretation

Equations and relationships

sin C = 1/n (glass–air)

Worked examples and applications

Common misconceptions

The glass–air equation is a special case, not the formula for every pair of media.

Examination technique

Show the sine value and the inverse-sine step, and label the answer in degrees.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.