Rays explained mirrors and lenses; they cannot explain why two slits paint stripes or why a soap bubble has colours. Here light is a wave: every point on a wavefront re-emits, path differences of whole wavelengths add up and half wavelengths cancel. One number rules the chapter — the path difference Δ, counted in wavelengths.
Every point a wavefront touches becomes a tiny source of secondary wavelets; the new front is their common envelope. When the front hits a slower medium, the wavelets there grow more slowly — the envelope tilts, and the whole beam bends. Refraction is not a rule; it is arithmetic.
Frequency never changes at a boundary — the glass cannot swallow crests. So v = fλ forces λ to shrink by n: watch the fronts bunch up below the surface.
Two slits, one wave — at a screen point P the two copies have walked different distances. The extra path is Δ = yd/D: whole wavelengths make a bright fringe, halves make darkness. Slide a thin glass slab over S₁ and you add optical path (n−1)t without moving anything — the whole pattern marches toward the covered slit.
A thickness t of glass holds the same light as (n−1)t extra of air — that is optical path. Shift = (n−1)tD/d, and in fringes simply (n−1)t/λ.
A soap film reflects twice — off its top and off its bottom. Ray 2 travels an extra optical path 2nt, and ray 1 picks up a free π flip at the denser top surface. Wavelengths that come out in step blaze back at you; the rest vanish into transmission. White light minus a few colours = the bubble’s shifting hues.
The π flip swaps the rules: what looks like the “in step” condition 2nt = mλ is actually dark. An ultra-thin film (t → 0) reflects nothing — a bursting bubble goes black just before it pops. Tilt θ and the in-film path shortens by the cos r factor, so every bright colour slides toward the blue — exactly why a soap bubble shimmers as it tilts.
One slit interferes with itself: pair each wavelet in the top half with one a/2 below it and whole strips cancel. Minima land at a·sinθ = mλ — note it is the dark condition, opposite in feel to the double slit. Squeeze the slit and the pattern defiantly widens.
The central maximum is twice as wide as every other bright band, and hogs ~84% of the light. This envelope also sits on top of any real double-slit pattern — where it dips to zero, interference orders go missing.
Every aperture diffracts, so a “point” star lands on your detector as a small blob. Two stars are just resolvable when the peak of one sits on the first dark ring of the other — closer than 1.22 λ/a apart and no lens on Earth can split them.
Your 2 mm pupil with 550 nm light: θmin ≈ 3.4×10⁻⁴ rad — headlights 1 km away merge into one. A telescope’s resolving power = a/1.22λ: aperture buys detail. A microscope’s limit is written in lengths instead, dmin ≈ λ/2NA — which is why oil immersion (NA > 1) and blue light see finer. (Blobs sketched with a sinc² profile; the true Airy disc differs only in detail — the 1.22 numbers are exact.)
Sound cannot be polarised; light can — proof its oscillation is sideways. A polaroid keeps only the E-field component along its axis, so intensity falls as cos²θ. Cross two sheets and the light dies… unless you sneak a third in between.
Brewster: reflected glare off water or glass is fully polarised when tan θB = n (water → 53°, glass → 56°) — then the reflected and refracted rays are exactly perpendicular. Polaroid sunglasses are built on this.
A warm-up, an open bench — a live double slit you must steer into each condition — then a JEE-Advanced exam bank. Collapse any rung you’re done with.
Drag P, tune d, λ, D — and when a task calls for it, switch the slab on over S₁ — then hit check.
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