Wave Optics
These are Apas Cloud services: they run on our servers for a signed-in member. The examples below are shown already made; sign in to edit and run your own.
ydse Apas Cloud
Young's double slit: slits d apart, the screen D away, wavelength lambda, all in one unit. The fringe width `beta` = lambda D / d; with a sheet of thickness t and index mu over one slit, the central fringe's `shift` = (mu - 1) t D / d towards that slit and `shiftFringes` = (mu - 1) t / lambda.
d (number) -- the slit separationD (number) -- the slit-to-screen distancelambda (number) -- the wavelength, in the same unitt (number) -- a sheet's thickness over one slit (optional, with mu)mu (number) -- the sheet's index (optional, with t)
ydsePoint Apas Cloud
A point at height y on the screen of Young's double slit: the path difference d y / D, its `order` in wavelengths, the `intensity` as a share of the maximum (cos^2 of half the phase difference) and the `fringe` in words: "bright" at a whole order, "dark" at a half-odd one, "between" otherwise.
d (number) -- the slit separationD (number) -- the slit-to-screen distancelambda (number) -- the wavelengthy (number) -- the point's height from the centre
wavefrontRefraction Apas Cloud
Huygens' refraction of a wavefront from n1 into n2 at i degrees: the record `r`, `speedRatio` = v2/v1 = n1/n2, `wavelengthRatio`, `totalInternal`.
n1 (number) -- the first indexn2 (number) -- the secondi (number) -- the angle of incidence in degrees
singleSlit Apas Cloud
Diffraction at a slit of width a on a screen D away: the record `theta1` (degrees) and `y1` of the first minimum, `width` = 2λD/a of the central maximum, `theta2` or "none".
a (number) -- the slit widthD (number) -- the screen distancelambda (number) -- the wavelength
singleSlitMinimum Apas Cloud
The angle of the n-th minimum, sin θ = nλ/a, in degrees, or "none".
a (number) -- the slit widthlambda (number) -- the wavelengthn (number) -- the order
singleSlitIntensity Apas Cloud
The single-slit intensity at θ degrees as a share of the centre, (sin β/β)² with β = πa sin θ/λ.
a (number) -- the slit widthlambda (number) -- the wavelengththeta (number) -- the angle in degrees
doubleSlitIntensity Apas Cloud
The double-slit intensity at θ as a share of the brightest fringe, cos²(πd sin θ/λ), under the single-slit envelope of width a (0 for narrow slits).
d (number) -- the slit separationa (number) -- the slit width (0 to ignore)lambda (number) -- the wavelengththeta (number) -- the angle in degrees
malus Apas Cloud
Malus's law, I0 cos²θ through an analyser at θ degrees to the polariser.
I0 (number) -- the intensity of the polarised lighttheta (number) -- the angle in degrees
brewster Apas Cloud
Brewster's angle, tan i_B = n2/n1: the record `iB` and `r` = 90 - iB, in degrees. NCERT XII Ex 10.6.
n2 (number) -- the index of the medium reflected fromn1 (number) -- the index light comes from (1)
rayleighLimit Apas Cloud
The Rayleigh limit of an aperture, 1.22 λ/D: the record `rad`, `deg`, `separation` at the distance given.
lambda (number) -- the wavelengthD (number) -- the aperturedistance (number) -- the distance of the objects (0)
fresnelDistance Apas Cloud
The Fresnel distance a²/λ beyond which a beam through an aperture spreads more than the aperture.
a (number) -- the aperturelambda (number) -- the wavelength
thinFilm Apas Cloud
A thin film of index μ and thickness t in reflected light at near-normal incidence: the record `path` = 2μt, `order` = 2μt/λ (half-odd bright, whole dark), `reflected` ("bright", "dark" or "partial"), `thinnestBright` = λ/4μ, `thinnestDark` = λ/2μ.
mu (number) -- the film's indext (number) -- the thicknesslambda (number) -- the wavelength in air
ydseOn Apas Cloud
Young's double slit at a readable scale (the true d, D and lambda written): the source S, the slits S1 and S2, the screen with its fringe strip (dark bands one fringe width apart from `ydse`), the central O, and when y is given the point P at that height with the two rays, the path difference Δ marked at S2, and its order and intensity in the caption; with t and mu a sheet over S1 with the central fringe shifted towards it. The summary is the fringe width (and the shift).
d (diagram) -- the diagram to draw ond (number) -- the slit separationD (number) -- the slit-to-screen distancelambda (number) -- the wavelength, in the same unity (number) -- the point P's height (optional)t (number) -- a sheet's thickness over S1 (optional, with mu)mu (number) -- the sheet's index (optional, with t)
wavefrontOn Apas Cloud
Wavefronts with their rays: plane fronts from a distant source, spherical fronts from a point source, cylindrical fronts from a slit; far away a front is nearly plane.
d (number) -- the diagramkind (text) -- "plane", "spherical" or "cylindrical"count (number) -- how many fronts (4)
huygensOn Apas Cloud
Huygens' construction of the refracted (NCERT Fig. 10.4) or reflected (Fig. 10.5) wavefront: the incident front AB, B reaching C in time τ while the wavelet from A grows to E, the new front CE, i and r marked; sin i/sin r = v1/v2 = n2/n1, or i = r.
d (number) -- the diagramkind (text) -- "refraction" or "reflection"i (number) -- the angle of incidence in degrees (5 to 85)n1 (number) -- the first index (1)n2 (number) -- the second index (1.5)
singleSlitOn Apas Cloud
Single-slit diffraction: the plane wave, the slit of width a, the screen D away with the minima marked and the central maximum 2λD/a wide, the rays to the first minimum, the (sin β/β)² intensity curve beside the screen.
d (number) -- the diagrama (number) -- the slit widthD (number) -- the screen distancelambda (number) -- the wavelength
fringeIntensityOn Apas Cloud
The double-slit intensity against the order y/β: 4I0 cos² fringes, and, when the slit width a is given, under the dashed single-slit envelope with the missing orders (d/a whole) named.
d (number) -- the diagramd (number) -- the slit separationlambda (number) -- the wavelengtha (number) -- the slit width (0 for narrow slits)orders (number) -- how many orders each side (4)
polarisationOn Apas Cloud
Polarisation: "wave" draws E oscillating in one plane and the end-on views of unpolarised and polarised light; "polaroids" draws unpolarised light through P1 (I0/2) and P2 at θ (Malus, (I0/2) cos²θ); "brewster" draws reflection at i_B = arctan(n2/n1) with the reflected and refracted rays at 90° and the polarisation marks.
d (number) -- the diagramkind (text) -- "wave", "polaroids" or "brewster"value (number) -- θ in degrees for the polaroids, n2 for Brewsterextra (number) -- I0 for the polaroids (1), n1 for Brewster (1)