Partial and Total Internal Reflection

Partial Reflection and Refraction:

• When light moves from a denser to a rarer medium, some of it is partially reflected back, while the rest refracts into the rarer medium.
• According to Snell’s Law, as the angle of incidence (i) increases, the angle of refraction (r) also increases.
• Since light moves from a denser to a rarer medium, it bends away from the normal (r > i).

Total Internal Reflection (TIR) and Critical Angle:

• At a certain critical angle, the angle of refraction becomes 90°, meaning the refracted ray grazes along the surface.
• If the angle of incidence is greater than the critical angle, all light is reflected back into the denser medium, causing Total Internal Reflection (TIR).

The critical angle is calculated using Snell’s Law:

\[_{1}\mathbf{n}_{2}=\quad\frac{\sin\mathbf{i}}{\sin\mathbf{r}}\] 

For total internal reflection, i = critical angle, r = 90⁰

\[_1\mathbf{n}_2=\frac{\sin\mathbf{i}}{\sin90^0}=\sin\mathbf{i}\]  (∵ sin 90⁰ = 1)

The refractive index of a medium determines the critical angle for TIR to occur.

Partial and total internal reflection

A rainbow is formed due to the dispersion, refraction, and total internal reflection of sunlight in water droplets.

• Raindrops act as tiny prisms, refracting and dispersing white light into different colours (VIBGYOR).
• Inside the droplet, Total Internal Reflection (TIR) redirects the light.
• As the light exits the droplet, it refracts again, forming a spectrum of seven colours.
• This combination of refraction, dispersion, and total internal reflection creates the beautiful rainbow seen after rainfall.

Rainbow production