Theory
Refraction
When a light ray passes from one transparent medium into another it changes direction at the interface because its speed changes. This bending is called refraction.
Snell's Law
\[\frac{\sin i}{\sin r} = \mu\]
μ is the refractive index of the second medium with respect to the first. Larger μ means more bending toward the normal.
Rectangular Glass Slab
A slab has two parallel surfaces. A light ray refracts on entering and again on exiting. Because the two refractions are equal and opposite, the emergent ray is parallel to the incident ray but shifted sideways. This sideways shift is the lateral displacement.
Lateral Displacement Formula
\[d = \frac{t\,\sin(i - r)}{\cos r}\]
- d — lateral displacement
- t — slab thickness
- i — angle of incidence
- r — angle of refraction (from Snell's law)
Dispersion and Wavelength
The refractive index depends slightly on wavelength (normal dispersion). Violet light has a higher μ than red, so it bends more and is displaced more.
Key Takeaways
- d ∝ t (thickness)
- d increases with the angle of incidence
- d increases with the refractive index
- Violet undergoes greater displacement than red
- Emergent ray is always parallel to the incident ray