| Material | Index n | Critical angle to air | Light slows to |
|---|
Same equation, opposite meaning. For a single slit, a sin θ = mλ gives the minima — the dark bands. For a double slit, d sin θ = mλ gives the maxima. Mixing them up is the single most common error in this topic.
Squeeze a beam through a smaller gap and it spreads more, not less. That is why a pinhole camera cannot be sharpened indefinitely by shrinking the pinhole, and why a telescope needs a big mirror to see fine detail rather than a good one.
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 that shortcut is already 1.9% wrong — small enough to look plausible and big enough to matter.
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 — which is why anti-reflection coatings were worth inventing.
Refraction is what happens at a boundary: light changes speed, so it changes direction, and Snell's law — n₁ sin θ₁ = n₂ sin θ₂ — is the bookkeeping. Going into a denser medium it bends toward the normal; coming out it bends away, and past a certain angle it cannot get out at all. Diffraction is what happens at an edge: light spreads because it is a wave, and the narrower the gap the more it spreads. One is about the interface, the other about the aperture, and they are often taught together only because both involve light not going straight.
Look into a pool 2 m deep and the bottom appears about 1.50 m down — the ratio of the two indices. Now look up from underwater: beyond 48.6° from vertical the surface turns into a mirror, and the entire sky is squeezed into a bright circle overhead. Same law, read in the other direction.
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 and treated as constant with wavelength within a calculation, so dispersion is described but not modelled. Intensity envelopes are drawn to show shape and position, not absolute brightness.
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