{"product_id":"light-optics-sticker-sheet","title":"Light \u0026 Optics Pixel Sticker Sheet – 12 Physics Stickers","description":"\u003cp\u003e12 pixel-art physics stickers on one A5 (5.83″ × 8.27″) white kiss-cut sheet: Light \u0026amp; Optics. Every character below has its own sticker page with the full physics panel.\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/scatterina-rayleigh-scattering-pixel-sticker\"\u003eScatterina\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eSmall particles and molecules scatter short wavelengths much more strongly, in proportion to one over wavelength to the fourth power. Blue light is scattered about 5.9 times more than red, which is why the sky looks blue.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eI\u003csub\u003es\u003c\/sub\u003e ∝ 1\/λ⁴\u003c\/strong\u003e\u003cbr\u003eI_s: power scattered by a molecule much smaller than the wavelength (W); λ: wavelength of the light (m)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/refracta-fermats-principle-pixel-sticker\"\u003eRefracta\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eLight takes the path between two points that takes the least time. That single rule gives Snell's law of refraction: light bends toward the slower medium, so that the sine of the angle divided by the speed is the same on both sides.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003esin θ\u003csub\u003e1\u003c\/sub\u003e\/v\u003csub\u003e1\u003c\/sub\u003e = sin θ\u003csub\u003e2\u003c\/sub\u003e\/v\u003csub\u003e2\u003c\/sub\u003e\u003c\/strong\u003e\u003cbr\u003eθ₁: angle of the path from the normal on the sand (light: in the first medium) (rad); θ₂: angle of the path from the normal in the water (light: in the second medium) (rad); v₁, v₂: speeds on each side (m\/s); n₁, n₂: refractive indices; c: speed of light in vacuum (m\/s); ds: element of path length (m)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/diagonix-maluss-law-pixel-sticker\"\u003eDiagonix\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eA polarizer passes the fraction cos²θ of already-polarized light. Two crossed polarizers block everything, but slip a third one between them at 45° and one-eighth of the original unpolarized light gets through.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eI = I\u003csub\u003e0\u003c\/sub\u003e cos²θ\u003c\/strong\u003e\u003cbr\u003eI: intensity after one ideal polariser (W\/m²); I₀: intensity arriving (unpolarised for the three-polariser line) (W\/m²); θ: angle between the light's polarisation and the polariser's transmission axis (rad); I_(out): intensity after the vertical, 45° and horizontal polarisers in turn (W\/m²)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/azurwake-cherenkov-radiation-pixel-sticker\"\u003eAzurwake\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eA charged particle moving through a medium faster than light travels in that medium emits light in a cone, like a sonic boom. The cone angle depends on the particle's speed and the refractive index, and Frank and Tamm's formula gives how many photons come out per unit length.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ecos θ = 1\/(nβ), β \u0026gt; 1\/n\u003c\/strong\u003e\u003cbr\u003eθ: angle between the emitted light and the particle's path (the wavefront cone has half-angle 90° − θ) (rad); n: refractive index of the medium, about 1.33 for water; β: particle speed as a fraction of c; N: number of photons emitted; x: distance travelled by the particle (m); λ: wavelength of the emitted light (m)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/halotra-22-degree-halo\"\u003eHalotra\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eThe real halo is made by millions of tiny hexagonal ice crystals in thin, high cirrus cloud, not by water droplets. Light entering one side face of a crystal and leaving by another passes through what is in effect a 60° prism. Every such prism has a minimum angle of deviation, and light piles up near it, so a bright ring appears at that angle from the Sun.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eD\u003csub\u003emin\u003c\/sub\u003e = 2 arcsin(n sin 30°) − 60°\u003c\/strong\u003e\u003cbr\u003eD\u003csub\u003emin\u003c\/sub\u003e: minimum deviation, the halo radius (degrees); n: refractive index of ice, about 1.31 for visible light; 30°: half the 60° prism angle between alternate faces\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/nicolette-nicol-prism\"\u003eNicolette\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eIn 1828 William Nicol of Edinburgh cut a calcite rhomb along a diagonal and cemented the halves back together with Canada balsam (Edinb. New Phil. J. 6, 83). Calcite splits light into an ordinary ray (n\u003csub\u003eo\u003c\/sub\u003e ≈ 1.658) and an extraordinary ray (n\u003csub\u003ee\u003c\/sub\u003e ≈ 1.486, along the slowest direction). Balsam sits between them at about 1.55. The ordinary ray, meeting the lower-index balsam at a steep angle, is totally internally reflected out of the side; the extraordinary ray passes. What leaves the end is linearly polarised.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003en\u003csub\u003eo\u003c\/sub\u003e \u0026gt; n\u003csub\u003ebalsam\u003c\/sub\u003e \u0026gt; n\u003csub\u003ee\u003c\/sub\u003e\u003c\/strong\u003e\u003cbr\u003en\u003csub\u003eo\u003c\/sub\u003e: ordinary refractive index of calcite, ≈ 1.658; n\u003csub\u003ebalsam\u003c\/sub\u003e: Canada balsam, ≈ 1.55; n\u003csub\u003ee\u003c\/sub\u003e: extraordinary index, ≈ 1.486 (sodium light)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/perota-fabry-perot\"\u003ePerota\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eTwo parallel, partly reflecting mirrors trap light that bounces back and forth. Only wavelengths that fit a whole number of half-waves into the gap build up and pass through; the rest cancel out. The transmission is a comb of sharp peaks, spaced by the free spectral range.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFSR = c\/(2nL)\u003c\/strong\u003e\u003cbr\u003eFSR: free spectral range, the frequency spacing between peaks (Hz); c: speed of light (m\/s); n: refractive index between the mirrors; L: mirror spacing (m)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/tweezra-optical-tweezers\"\u003eTweezra\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eFocus a laser beam tightly through a microscope lens and a small transparent bead is pulled towards the brightest point and held there. Light bends as it passes through the bead, and the change in its momentum pushes back on the bead. For a bead that bends light more than its surroundings, the net gradient force points up the intensity gradient, towards the focus. Arthur Ashkin accelerated and trapped particles with radiation pressure in 1970 (Phys. Rev. Lett. 24, 156), and with colleagues demonstrated the single-beam gradient trap, the optical tweezers, in 1986 (Opt. Lett. 11, 288).\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eF\u003csub\u003egrad\u003c\/sub\u003e ∝ ∇I\u003c\/strong\u003e\u003cbr\u003eF\u003csub\u003egrad\u003c\/sub\u003e: gradient force on the bead (N); ∇I: gradient of the light intensity (W\/m³)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/pockella-pockels-effect\"\u003ePockella\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eSome crystals without a centre of symmetry change their refractive index in direct proportion to an applied electric field. Friedrich Pockels studied this linear electro-optic effect in 1893. Put such a crystal between crossed polarisers and a voltage can switch light on and off in nanoseconds.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eΔn ∝ E\u003c\/strong\u003e\u003cbr\u003eΔn: change in refractive index; E: applied electric field (V\/m)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/infrara-herschel-infrared\"\u003eInfrara\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eIn 1800 William Herschel placed thermometers in the colours of a prism spectrum and found the temperature rose from violet to red. Then he moved one past the red end, where no light could be seen, and it rose further still (“Experiments on the Refrangibility of the Invisible Rays of the Sun”, Phil. Trans. R. Soc. 90, 284). The Sun emits invisible rays beyond the red: infrared.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eλ\u003csub\u003eIR\u003c\/sub\u003e \u0026gt; λ\u003csub\u003ered\u003c\/sub\u003e ≈ 0.7 µm\u003c\/strong\u003e\u003cbr\u003eλ\u003csub\u003eIR\u003c\/sub\u003e: infrared wavelengths, about 0.7 µm to 1 mm; λ\u003csub\u003ered\u003c\/sub\u003e: long-wavelength end of the visible spectrum\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/mirrorspin-foucault-speed-of-light\"\u003eMirrorspin\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eIn 1862 Léon Foucault measured the speed of light in a laboratory with a rapidly rotating mirror (Comptes rendus 55, 501). Light reflects off the spinning mirror to a distant fixed mirror and back. In the round-trip time the rotating mirror turns a tiny angle, so the returning spot lands slightly displaced. From the displacement, the path length and the spin rate he got c = 298 000 ± 500 km\/s, close to the modern value.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eΔα = 2ωD\/c\u003c\/strong\u003e\u003cbr\u003eΔα: angle the mirror turns during the round trip (rad); the returning beam is deflected by 2Δα; ω: angular speed of the mirror (rad\/s); D: distance to the fixed mirror (m); c: speed of light (m\/s)\u003c\/p\u003e\u003ch3\u003e\u003ca href=\"https:\/\/pixelatedphysics.com\/products\/christiaan-huygens-sticker-every-point-a-source-physics-sticker\"\u003eChristiaan Huygens\u003c\/a\u003e\u003c\/h3\u003e\u003cp\u003eHuygens' principle treats every point on a wavefront as a source of small spherical wavelets. After a short time, the new wavefront is the surface that touches all of those wavelets, which explains reflection and refraction.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003er = vΔt\u003c\/strong\u003e\u003cbr\u003er: radius of each secondary wavelet after time \\Delta t (m); v: wave speed in the medium (m\/s); Δ t: time step (s)\u003c\/p\u003e","brand":"Printify","offers":[{"title":"White \/ Kiss-Cut \/ 5.83″ × 8.27″","offer_id":50966943006823,"sku":"20684385716945323770","price":19.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/11619963504391612442_2048.jpg?v=1793676469","url":"https:\/\/pixelatedphysics.com\/products\/light-optics-sticker-sheet","provider":"Pixelated Physics","version":"1.0","type":"link"}