Light changes speed when crossing boundaries between optical media, producing refraction and total internal reflection. Calculating refractive index via Snell's Law ($n = \sin i / \sin r$) and critical angles ($n = 1/\sin c$) governs fiber optic communications in Cambridge IGCSE Physics.

When light enters an optically denser medium (such as from air into glass), its speed decreases, causing the ray to bend toward the normal ($i > r$).

Snell's Law Equation

The ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) defines the refractive index ($n$):

Also defined by light speed ratio: $n = \frac{c_{\text{vacuum}}}{v_{\text{medium}}}$.

When light travels from an optically denser medium toward a less dense medium (e.g. glass to air):

1. $i < c$: Light refracts into air away from the normal, with a weak reflected ray.
2. $i = c$ (Critical Angle): Refracted ray travels along the boundary surface ($r = 90^\circ$).
3. $i > c$ (Total Internal Reflection): Zero refraction occurs; $100\%$ of light reflects back inside the denser medium.

Critical Angle Equation

Total internal reflection is utilized in optical fibres for high-speed internet data transmission and medical endoscopes. Light entering a glass fiber core strikes the outer cladding interface at an angle $i > c$, trapping light inside via repeated TIR over kilometers with minimal signal attenuation.

Advanced Physical Analysis

Monochromatic light consists of a single frequency and wavelength. Total internal reflection occurs when angle of incidence exceeds critical angle ($c = \sin^{-1}(1/n)$) inside an optically denser medium.

Extended Experimental Procedures and Quantitative Analysis

Experimental investigations require meticulous measurement and systematic error reduction. Digital timers, micrometers, and vernier calipers reduce uncertainty. Data analysis involves plotting linear graphs, calculating gradients to represent rate of change or physical constants, and comparing experimental values against theoretical expectations to quantify percentage error ($|\text{Exp} - \text{Theo}| / \text{Theo} \times 100\%$).

Refraction obeys Snell's Law ($n = \sin i / \sin r$). Total Internal Reflection occurs when $i > c$, governed by $n = 1/\sin c$, enabling fiber optic data transmission.