Q.The critical angles for glass (μ_g = 1.5), water (μ_w = 1.33) and diamond (μ_D = 2.42) are θ_g, θ_w and θ_D respectively. Arrange the angles in descending order.

Critical Angle Comparison: From Intuition to Precision

Imagine you're standing at the edge of a swimming pool, looking down at a coin at the bottom. The coin appears closer to the surface than it actually is. That's refraction — light bends when it moves from water into air. Now imagine tilting your head so you're looking at the coin from a very shallow angle. At some point, the coin suddenly vanishes. You can't see it anymore, no matter how hard you try. That vanishing point is the critical angle.

The Intuition

Light travels at different speeds in different materials. When it crosses from a denser medium (like water or glass) into a rarer medium (like air), it bends away from the normal (the imaginary line perpendicular to the surface). The larger the angle of incidence (the angle at which light hits the boundary), the more it bends away.

At a certain angle of incidence, the refracted ray bends so much that it runs exactly along the surface — it makes a 90° angle with the normal. That's the critical angle. If you increase the angle of incidence even slightly beyond this, the light can't escape at all. It reflects back into the denser medium, a phenomenon called total internal reflection.

The Precise Statement

The critical angle ($\theta_c$) is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is exactly 90°.

Mathematically, from Snell's law:

Let medium 1 be the denser medium (refractive index $n_1$) and medium 2 be the rarer medium (refractive index $n_2$, with $n_2 < n_1$). At the critical angle, $\theta_1 = \theta_c$ and $\theta_2 = 90^\circ$, so $\sin \theta_2 = 1$. This gives:

Where:

• $\theta_c$ = critical angle
• $n_1$ = refractive index of the denser medium
• $n_2$ = refractive index of the rarer medium

What This Tells You

The critical angle depends only on the ratio of the two refractive indices. A larger difference between $n_1$ and $n_2$ means a smaller critical angle — light is more "trapped" inside the denser medium. For example: