| Material | Index n | Critical angle to air | Light slows to |
|---|
Light changes speed, so it changes direction. Into a denser medium it bends toward the normal; past a critical angle it cannot get out at all. Snell’s law is the bookkeeping.
Light spreads because it is a wave, and the narrower the gap the more it spreads. About the aperture, not the interface.
The s and p components separately for a transparent boundary; at Brewster’s angle arctan(n₂/n₁) the p component is exactly zero.
For a single slit a sin θ = mλ gives the minima; for a double slit d sin θ = mλ gives the maxima.
Squeeze a beam through a smaller gap and it spreads more, not less: diffraction angle goes as wavelength over aperture. A pinhole camera cannot be sharpened indefinitely by shrinking the pinhole, and a telescope needs a big mirror to see fine detail rather than a good one: no magnification substitutes for aperture.
Replacing sin θ with θ is fine for a double slit at a couple of degrees. On a 600 lines/mm grating the first order sits near 19°, where the shortcut is already 1.9% wrong: small enough to look plausible and big enough to matter.
The index of glass is a little higher for short wavelengths. One surface barely shows it; a prism uses two, angled so the bends add. A 60° crown-glass prism fans the visible over about 1.6°: a rainbow 27 mm tall on a wall a metre away. The Abbe number measures it (lower spreads more): flint glass at 36 spreads colour about twice as much as crown at 64, which is why achromatic lenses pair the two.
An air-to-glass surface reflects about 4% at normal incidence. A lens with six uncoated elements has twelve such surfaces and loses roughly 40% of the light: why anti-reflection coatings were worth inventing.
It travels more slowly in a denser medium, and a wavefront arriving at an angle enters at one edge before the other. That edge slows first, so the wavefront pivots, like a trolley whose left wheel hits gravel before the right. Total internal reflection is mostly for optical fibre: light entering the core at a shallow enough angle bounces along for kilometres.
Near Brewster’s angle (about 53° for water) the reflected light is almost entirely polarised in one direction, so a filter turned the other way removes nearly all of it. The calculator shows the s and p components separately.
The Fresnel equations here are the real-valued ones for transparent dielectrics. Metals have a complex refractive index and a different reflectance curve: do not use these numbers for mirrors or anything coloured by absorption.
It travels more slowly in a denser medium, and a wavefront arriving at an angle enters the new medium at one edge before the other. That edge slows first, so the wavefront pivots — exactly like a trolley whose left wheel hits gravel before the right one.
Optical fibre, mostly. Light entering the core at a shallow enough angle can never escape through the wall, so it bounces along the fibre for kilometres. It is also why a diamond sparkles: a critical angle of 24° means light rattles around inside before finding a facet it can leave through.
Near Brewster's angle — about 53° for water — the reflected light is almost entirely polarised in one direction, so a filter turned the other way removes nearly all of it. The calculator shows the s and p components separately; at Brewster's angle the p component is exactly zero.
No. The Fresnel equations here are the real-valued ones for transparent dielectrics. Metals have a complex refractive index and a different reflectance curve, so do not use these numbers for mirrors or for anything coloured by absorption.
Monochromatic light, flat boundaries, and non-absorbing non-magnetic materials. The Fresnel equations used are the real-valued dielectric forms, so they do not apply to metals, absorbing media or thin-film coatings, where interference between surfaces dominates. Diffraction results use the Fraunhofer (far-field) condition, which assumes the screen is far enough away that the wavefronts arriving at it are effectively flat — close to the aperture the Fresnel regime applies instead and the pattern differs. Refractive indices are quoted at 589 nm. Refraction treats them as constant with wavelength; the prism models dispersion with a two-term Cauchy curve fitted to each material's Abbe number, which follows the full Sellmeier curves to within 0.0003 for glass and silica and 0.002 for diamond across the visible. Intensity envelopes are drawn to show shape and position, not absolute brightness.
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