Tag: physics
All the articles with the tag "physics".
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The colors of a soap film
Posted on:A soap film reflects a spectrum that is a single cosine in the reciprocal of the wavelength, so its color is a fixed white minus the cosine transform of the CIE color-matching functions, evaluated at twice the film's optical thickness. The computed sequence agrees with Newton's table of thin-film colors, and the fade to white in thick films is the decay of the transform.
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The kaleidoscope in an elevator
Posted on:Two mirrors that meet at an angle place every image on a circle around the line where they meet. Elevator mirrors a tenth of a degree off parallel form a kaleidoscope with 3600 sectors centered almost a kilometer away, which bends the mirror tunnel and lets you read the tilt off a photograph.
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The Ehrenfest urn
Posted on:N numbered balls in two urns, one moved at random per step, is the random walk on the corners of the N-cube. Its equilibrium is the binomial, the mean imbalance decays like (1 − 2/N)^t, and the expected time to return to the all-in-one-urn state is exactly 2^N.
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Pendulum period
Posted on:The pendulum period grows with amplitude; 2π√(L/g) is only the zeroth term. The exact period is an elliptic integral, and Gauss's arithmetic–geometric mean evaluates it in five iterations.
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The curve of fastest descent
Posted on:The wire carrying a sliding bead between two points in the least time is a cycloid arc, not the straight line. Optics finds it, convexity proves it, and the same arc is the tautochrone.
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Euler's identity
Posted on:e^{iπ} + 1 = 0 is the θ = π case of Euler's formula e^{iθ} = cos θ + i sin θ, the point on the unit circle at angle θ. Three derivations: geometric, as a limit, and by power series.
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Heisenberg uncertainty as Fourier duality
Posted on:The uncertainty principle is not a measurement artifact but a property of any wave: a packet narrow in x is spread in p, and σx · σp ≥ ℏ/2 with equality exactly for Gaussians.
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An analogy for the Doppler effect
Posted on:A simple analogy to explain the Doppler effect using the concept of throwing balls between two people. Designed to make the physics concept intuitive and accessible to a layperson.