Quick questions on Wave model of light: diffraction, interference and polarisation, HSC Physics Module 7

Newton's particle (corpuscular) picture of light explained reflection and refraction but failed to predict diffraction and interference. By 1801 Thomas Young's double-slit experiment demonstrated that light produces interference fringes, which only waves can do. The wave model dominated nineteenth-century optics and motivated Maxwell's identification of light as an EM wave.

Monochromatic, coherent light passing through two narrow slits separated by $d$ produces alternating bright and dark fringes on a screen at distance $L$. Bright fringes occur where the path difference equals a whole number of wavelengths:

A single slit of width $a$ produces a broader pattern with a wide central maximum and narrow, rapidly weakening side maxima. The dark fringes occur where:

Light is a transverse EM wave: $\vec{E}$ and $\vec{B}$ are perpendicular to the direction of propagation. Unpolarised light contains $\vec{E}$ vibrating in all directions perpendicular to the wave; a polarising filter passes only the component along its transmission axis.

If polarised light of intensity $I_0$ encounters a second polariser whose transmission axis makes angle $\theta$ with the first:

Unpolarised light at $120$ W m$^{-2}$ enters two polarisers whose axes are at $45^\circ$ to each other.

The double-slit condition gives maxima; for a single slit of width $a$ the same equation form gives minima.

Always halve first, then apply Malus's law on subsequent polarisers.

Path difference of $m \lambda$ equals phase difference of $2 \pi m$.

They are the same underlying superposition. Diffraction is interference from a continuous range of source points; "double-slit interference" is interference from two discrete sources.