State the meaning of critical angle

3.2.2 Refraction of Light

Objective

State the meaning of the critical angle.

Definition of Critical Angle

The critical angle, denoted by \$c\$, is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is \$90^{\circ}\$. At this angle the refracted ray travels along the boundary between the two media.

Mathematical Expression

When light passes from a medium of refractive index \$n1\$ (denser) to a medium of refractive index \$n2\$ (rarer) with \$n1 > n2\$, the critical angle is given by:

\$\sin c = \frac{n2}{n1}\$

If the angle of incidence exceeds \$c\$, total internal reflection occurs.

Typical Critical Angles

Key Points to Remember

• The critical angle exists only when light travels from a denser to a rarer medium (\$n1 > n2\$).
• At the critical angle the refracted ray makes \$90^{\circ}\$ with the normal, travelling along the interface.
• Angles of incidence greater than the critical angle result in total internal reflection.
• The critical angle is inversely related to the difference in refractive indices: larger difference → smaller critical angle.