Optics & Waves

Light, lenses, mirrors, sound and wave behaviour

Optics & Waves covers the key formulas behind light, lenses, mirrors, sound, and wave behaviour, from wave speed and Snell’s Law to diffraction and the Doppler effect. It’s a practical reference for students, exam preparation, and anyone applying physics in real-world settings, helping you solve problems, understand how waves behave, and make sense of everyday technologies like cameras, glasses, and sensors.

Wave Speed

v = f\lambda

Speed of a wave from frequency and wavelength.

Wave Period

T = \frac{1}{f}

Time for one complete oscillation.

Snell's Law

n_1\sin\theta_1 = n_2\sin\theta_2

Refraction of light between two media.

Refractive Index

n = \frac{c}{v}

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

Critical Angle

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

Angle beyond which total internal reflection occurs.

Thin Lens Equation

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Relates focal length to object and image distances.

Lens Magnification

M = -\frac{d_i}{d_o}

Image size relative to object size.

Mirror Equation

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Focal length relation for curved mirrors.

Lens Power

P = \frac{1}{f}

Optical power in dioptres (f in metres).

Diffraction Grating

d\sin\theta = m\lambda

Condition for constructive interference maxima.

Double-Slit Fringe Spacing

\Delta y = \frac{\lambda L}{d}

Spacing of interference fringes on a screen.

Doppler Effect (Sound)

f' = f\frac{v \pm v_o}{v \mp v_s}

Observed frequency shift from relative motion.

Sound Intensity Level

\beta = 10\log_{10}\frac{I}{I_0}

Loudness in decibels relative to threshold.

Photon Energy

E = hf

Energy of a single photon.

Photon Energy (Wavelength)

E = \frac{hc}{\lambda}

Photon energy from its wavelength.

Malus's Law

I = I_0\cos^2\theta

Intensity of polarised light through a polariser.

Standing Wave (String)

f_n = \frac{nv}{2L}

Harmonic frequencies of a fixed string.

Wave Speed on a String

v = \sqrt{\frac{T}{\mu}}

Speed depends on tension and linear density.