Refraction of Light Fundamentals

Refraction and Total Internal Reflection (TIR)

Laws of Refraction

1) Snell’s Law:

\[ \frac{\sin i}{\sin r} = \text{constant} = n_{21} = \frac{v_1}{v_2} \]

The constant is called the refractive index of medium 2 with respect to medium 1.

2) Coplanarity:

Incident ray, refracted ray, and normal all lie in the same plane.

Refractive index measures how much light slows down in a medium. Higher refractive index → slower light and more bending.

Absolute Refractive Index

If refraction happens from vacuum or air:

\[ n_1 = \frac{c}{v_1}, \quad n_2 = \frac{c}{v_2} \]

Where \(c\) is the speed of light in vacuum.

Relative Refractive Index

\[ \frac{n_2}{n_1} = \frac{v_1}{v_2} = n_{21} \]

\[ n_{21} = \frac{n_2}{n_1} \]

Refraction Cases

Rarer to Denser Medium

Light bends towards the normal:

\[ i > r, \quad \frac{\sin i}{\sin r} > 1 \]

\[ n = \frac{c}{v} \]

Denser to Rarer Medium

Light bends away from the normal:

\[ i < r, \quad \frac{\sin i}{\sin r} < 1 \]

\[ \frac{1}{n} = \frac{v}{c} \]

Lateral Shift in Glass Slab

When light passes through a parallel-sided slab, it emerges parallel but shifted sideways.

\[ L = \sin(i - r) \cdot \frac{t}{\cos r} \]

Where:

• \(L\) = lateral shift
• \(t\) = thickness of slab
• \(i\) = angle of incidence
• \(r\) = angle of refraction

Reversibility of Light

If the direction of light is reversed, it retraces the same path.

This principle is known as Reversibility of Light.