Refraction and Total Internal Reflection (TIR)
Laws of Refraction
Snell’s Law:
\[ \frac{\sin i}{\sin r} = n_{21} = \frac{v_1}{v_2} \]
The constant represents refractive index.
Coplanarity:
Incident ray, refracted ray and normal lie in same plane.
Higher refractive index → slower light → more bending.
Rarer → Denser
Ray bends towards normal
\[ i > r, \quad \frac{\sin i}{\sin r} > 1 \]
\[ n = \frac{c}{v} \]
Lateral Shift
Emergent ray is parallel but shifted.
\[ L = \sin(i - r)\frac{t}{\cos r} \]
- \(L\): shift
- \(t\): thickness
- \(i, r\): angles
Absolute Refractive Index
\[ n_1 = \frac{c}{v_1}, \quad n_2 = \frac{c}{v_2} \]
\(c\) = speed of light in vacuum
Relative Refractive Index
\[ \frac{n_2}{n_1} = \frac{v_1}{v_2} \]
\[ n_{21} = \frac{n_2}{n_1} \]
Denser → Rarer
Bends away from normal
\[ i < r, \quad \frac{\sin i}{\sin r} < 1 \]
\[ \frac{1}{n} = \frac{v}{c} \]
Reversibility of Light
Light retraces same path if direction reversed.
Important concept for ray optics problems.
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