Total Internal ReflectionJEE Main

Concept

When light travels from a denser medium to a rarer one, it bends away from the normal. Past a certain critical angle the refracted ray would exceed 90° — so instead the light is totally internally reflected back into the denser medium.

Key formula

Derivation

Snell's law $n_1\sin\theta_1 = n_2\sin\theta_2$ shows the refracted angle grows faster than the incident one when $n_1 > n_2$.

At $\theta_2 = 90^\circ$ the ray skims the surface; the corresponding incidence is the critical angle $\theta_c = \sin^{-1}(n_2/n_1)$. Beyond it, no refraction is possible and all the light reflects.

Scenarios to explore

• Total Internal Reflection — Critical angle and TIR at an interface.

Real-world applications

• Optical fibres guiding light over long distances.
• Sparkle of diamonds (tiny $\theta_c \approx 24°$).
• Prisms in binoculars and periscopes.

JEE exam tips

• TIR requires light in the denser medium and $\theta_i > \theta_c$.
• Smaller critical angle ⇒ easier TIR ⇒ more brilliance (diamond).
• $\theta_c = \sin^{-1}(1/n)$ when the second medium is air.

Common mistakes

• Expecting TIR going from rarer to denser (impossible).
• Swapping $n_1$ and $n_2$ in the ratio.
• Forgetting TIR needs $\theta_i > \theta_c$, not just $\ge$.

Exam traps to avoid

• At exactly $\theta_c$ the ray grazes along the boundary, not reflected yet.
• A higher $n_1$ lowers the critical angle.