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

When light enters a rarer medium from a denser medium, it gets partially reflected i.e. part of the light gets reflected and comes back into the denser medium as per laws of reflection. This is called partial reflection.

For a particular value of i, the value of r becomes equal to 90°. This value of i is called the critical angle.

For angles of incidence larger than the critical angle, the angle of refraction is larger than 90°. Such rays return to the denser medium. Thus, all the light gets reflected back into the dense medium. This is called total internal reflection.

• Light going from a denser to a rarer medium partly reflects and partly bends away from the normal.
• If we keep increasing the angle of incidence, the refracted ray becomes 90° at a certain point — this is the critical angle.
• Beyond the critical angle, all light reflects back into the denser medium — this is total internal reflection.
• A rainbow forms due to refraction, dispersion, and total internal reflection of sunlight in raindrops.
• Snell’s law explains how the angle of refraction depends on the angle of incidence and the refractive index.