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Optics & Waves

Light, lenses, mirrors, sound and wave behaviour

Wave Speed

Basic
v=fλv = f\lambda

Speed of a wave from frequency and wavelength.

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Wave Period

Basic
T=1fT = \frac{1}{f}

Time for one complete oscillation.

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Snell's Law

Intermediate
n1sinθ1=n2sinθ2n_1\sin\theta_1 = n_2\sin\theta_2

Refraction of light between two media.

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Refractive Index

Intermediate
n=cvn = \frac{c}{v}

Ratio of light speed in vacuum to that in a medium.

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Critical Angle

Advanced
θc=sin1n2n1\theta_c = \sin^{-1}\frac{n_2}{n_1}

Angle beyond which total internal reflection occurs.

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Thin Lens Equation

Intermediate
1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Relates focal length to object and image distances.

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Lens Magnification

Intermediate
M=didoM = -\frac{d_i}{d_o}

Image size relative to object size.

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Mirror Equation

Intermediate
1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Focal length relation for curved mirrors.

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Lens Power

Basic
P=1fP = \frac{1}{f}

Optical power in dioptres (f in metres).

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Diffraction Grating

Advanced
dsinθ=mλd\sin\theta = m\lambda

Condition for constructive interference maxima.

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Double-Slit Fringe Spacing

Advanced
Δy=λLd\Delta y = \frac{\lambda L}{d}

Spacing of interference fringes on a screen.

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Doppler Effect (Sound)

Advanced
f=fv±vovvsf' = f\frac{v \pm v_o}{v \mp v_s}

Observed frequency shift from relative motion.

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Sound Intensity Level

Intermediate
β=10log10II0\beta = 10\log_{10}\frac{I}{I_0}

Loudness in decibels relative to threshold.

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Photon Energy

Intermediate
E=hfE = hf

Energy of a single photon.

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Photon Energy (Wavelength)

Intermediate
E=hcλE = \frac{hc}{\lambda}

Photon energy from its wavelength.

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Malus's Law

Advanced
I=I0cos2θI = I_0\cos^2\theta

Intensity of polarised light through a polariser.

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Standing Wave (String)

Advanced
fn=nv2Lf_n = \frac{nv}{2L}

Harmonic frequencies of a fixed string.

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Wave Speed on a String

Advanced
v=Tμv = \sqrt{\frac{T}{\mu}}

Speed depends on tension and linear density.

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