Key Equations

Waves - OCR A-Level Physics

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Wave equation
$$v = f\lambda$$
  • Where:
    • $v$ = m \(s^{-1}\)
    • $f$ = Hz
    • $\lambda$ = m
Applies to all waves. Speed depends on medium, not source.
Period–frequency relationship
$$T = \frac{1}{f}$$
  • Where:
    • $T$ = s
    • $f$ = Hz
Period is the reciprocal of frequency.
Snell's law of refraction
$$n_{1} \sin\theta_{1} = n_{2} \sin\theta_{2}$$
  • Where:
    • $n$ = dimensionless
    • $\theta$ = degrees or radians
n = c/v for each medium. Angles measured from the normal.
Critical angle
$$\sin\theta_{c} = \frac{n_{2}}{n_{1}}$$
  • Where:
    • $\theta_c$ = degrees or radians
Derived from Snell's law with θ₂ = 90°. For glass–air: sin θ_c = 1/n_glass. Must be memorised.
Young's double-slit equation
$$\lambda = \frac{ax}{D}$$
  • Where:
    • $\lambda$ = m
    • $a$ = m
    • $x$ = m
    • $D$ = m
Requires D >> a. x is the fringe spacing between adjacent bright fringes.
Diffraction grating equation
$$d\sin\theta = n\lambda$$
  • Where:
    • $d$ = m
    • $\theta$ = degrees or radians
    • $\lambda$ = m
d = 1/(lines per metre). n is the order number (integer). Maximum order when sin θ = 1.
Intensity–amplitude relationship
$$I \propto A^{2}$$
  • Where:
    • $I$ = W \(m^{-2}\)
    • $A$ = m
Doubling amplitude quadruples intensity. Applies to all progressive waves.
Refractive index
$$n = \frac{c}{v}$$
  • Where:
    • $n$ = dimensionless
    • $c$ = m \(s^{-1}\)
    • $v$ = m \(s^{-1}\)
c = speed of light in vacuum, v = speed of light in the medium. n is always ≥ 1.
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