Total Internal ReflectionJEE Main

Critical angle & TIR — interactive Physics simulation for IIT-JEE.

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

n_1\sin\theta_c = n_2\sin 90^\circ \;\Rightarrow\; \theta_c = \sin^{-1}\!\left(\frac{n_2}{n_1}\right)

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.
Glass to air: total reflection — Beyond 41.8° a ray in glass cannot escape into air.
Diamond traps the light — A critical angle of only 24.6° is why diamonds sparkle.
Water to air: just refracts — The critical angle for water is 48.8°; at 40° the ray leaves.

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.