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Waves & Optics — Formula Cheat Sheet
Every key formula for Waves & Optics, with what it means and where it comes from.
| Formula | What it means | Topic |
|---|---|---|
| d sin(theta) = m lambda | Bright fringe positions in a double slit, with m = 0, 1, 2, ... for successive bright fringes. | Interference and Diffraction |
| delta x = lambda L / d | Spacing between bright fringes on a screen distance L from slits separated by d. | Interference and Diffraction |
| a sin(theta) = lambda | First minimum of a single slit of width a. | Interference and Diffraction |
| 1/f = 1/do + 1/di | Thin lens and mirror equation, with object distance do, image distance di and focal length f. | Lenses and Mirrors |
| m = hi / ho = -di / do | Magnification equals image height over object height, and equals minus image distance over object distance. | Lenses and Mirrors |
| f = R / 2 | Focal length of a spherical mirror equals half its radius of curvature. | Lenses and Mirrors |
| angle of incidence = angle of reflection | Law of reflection for a ray striking a smooth surface. | Reflection and Refraction of Light |
| n1 sin(theta1) = n2 sin(theta2) | Snell's law of refraction, with refractive indices n1 and n2. | Reflection and Refraction of Light |
| n = c / v | Refractive index equals speed of light in a vacuum divided by speed in the medium. | Reflection and Refraction of Light |
| sin(theta_c) = n2 / n1 | Critical angle for total internal reflection, with n1 greater than n2. | Reflection and Refraction of Light |
| v = f lambda | Speed of sound equals frequency times wavelength. | Sound Waves |
| v = 331 + 0.6 T | Approximate speed of sound in air in m/s, with T in degrees Celsius. | Sound Waves |
| f' = f v / (v - vs) | Observed frequency for a source moving toward a stationary observer at speed vs. | The Doppler Effect |
| f' = f v / (v + vs) | Observed frequency for a source moving away from a stationary observer. | The Doppler Effect |
| f' = f (v + vo) / v | Observed frequency for an observer moving toward a stationary source at speed vo. | The Doppler Effect |
| v = f lambda | Wave speed equals frequency times wavelength. | Waves: Amplitude, Frequency and Wavelength |
| T = 1 / f | Period equals one divided by frequency. | Waves: Amplitude, Frequency and Wavelength |
| f = 1 / T | Frequency equals one divided by period. | Waves: Amplitude, Frequency and Wavelength |
| f′ = f × v ÷ (v − v_s) | A source moving toward you squeezes the waves together and raises the pitch; moving away stretches them and lowers it. | Doppler Effect Calculator |
| 1 ÷ f = 1 ÷ d_obj + 1 ÷ d_img | For a thin lens or mirror the reciprocals of focal length, object distance and image distance add up, and a negative result means a virtual image. | Lens and Mirror Calculator |
| n = c ÷ v | The refractive index is how many times slower light travels in a material than in a vacuum. | Refractive Index Calculator |
| n₁ sin θ₁ = n₂ sin θ₂ | Light changes direction at a boundary because its speed changes; the angles are measured from the normal line. | Snell's Law Calculator |
| c = λ × f | Light in a vacuum always travels at the same speed, so a longer wavelength means a lower frequency and vice versa. | Speed of Light / Frequency–Wavelength Calculator |
| y = m × λ × L ÷ d | In a double-slit pattern the bright fringes spread out with longer wavelengths, longer screens and narrower slit spacing. | Wave Interference Calculator |
| v = f × λ | A wave's speed equals its frequency times its wavelength, so faster waves at the same frequency are longer. | Wave Speed Calculator |