State the meaning of critical angle

3.2.2 Refraction of Light

What is Refraction?

When light passes from one medium to another (e.g. from air to water), its speed changes, causing the light ray to bend. This bending is called refraction 🌊. The amount of bending depends on the optical densities of the two media, described by their refractive indices ($n$).

Snell’s Law

Snell’s Law gives the relationship between the angles of incidence ($\theta_1$) and refraction ($\theta_2$):

$\,n_1 \sin \theta_1 = n_2 \sin \theta_2\,$

• $n_1$ and $n_2$ are the refractive indices of the first and second medium.
• If $n_2 > n_1$, the ray bends towards the normal (downwards).
• If $n_2 < n_1$, the ray bends away from the normal (upwards).

Critical Angle

The critical angle ($\theta_c$) is the specific angle of incidence at which the refracted ray travels along the boundary between the two media. For angles larger than $\theta_c$, the light is totally internally reflected back into the first medium. This happens only when the light moves from a denser medium to a less dense one ($n_1 > n_2$).

Mathematically, the critical angle is found from:

$\,n_1 \sin \theta_c = n_2\, \;\;\;\;\; \Rightarrow \;\;\;\;\; \theta_c = \arcsin\!\left(\dfrac{n_2}{n_1}\right)\,$

1. Identify $n_1$ (denser medium) and $n_2$ (less dense medium).
2. Compute $\dfrac{n_2}{n_1}$.
3. Take the arcsine to find $\theta_c$.

Practical Example & Analogy

Imagine a swimmer moving from a shallow pool ($n_1 = 1.33$) to a deep pool ($n_2 = 1.00$). If the swimmer enters at a shallow angle, they will be pushed towards the surface (bending away). At a certain angle, the swimmer will glide along the surface—this is the critical angle. If they try to go even shallower, they will be reflected back into the shallow pool (total internal reflection) 🚣‍♂️.

Refractive Indices of Common Media

Key Takeaway

Critical angle is the maximum angle of incidence for which light can still refract into the second medium. Beyond this angle, light is reflected entirely back into the first medium. Understanding this concept helps explain phenomena like the bright edge of a swimming pool or the rainbow effect in a prism 🌈.