Optics

The big picture

A ray diagram predicts where an image forms. A wave model predicts whether light reinforces, cancels or spreads. The skill is choosing which picture answers the question, then keeping the geometry and sign convention consistent.

Follow refraction into image formation before turning to interference and diffraction. In a spectrum, distinguish the spacing of line centres from their width: a pattern can be widely spread and still fail to resolve nearby wavelengths.

What to read, and why

Start at the first stage if the subject is new. Otherwise, use the descriptions to find the missing step in your understanding. All chapter explanations are open; the labels identify chapters whose solutions and answer checks are also free.

1. STAGE 1

   Build the image

   Track angles at interfaces and use a stated sign convention for curved surfaces, lenses and mirrors.

   Refraction, internal reflection and dispersion →Draw the normal, trace each boundary and let the geometry decide which formula applies.9 worked examples · 7 checks · Complete free chapterImages at refracting surfaces and thin lenses →Use one sign convention, construct the rays and carry intermediate images through the system.9 worked examples · 8 checks · Open explanation · member practiceSpherical mirrors: images, signs and moving objects →Keep the incident-light axis fixed and use reflection geometry to check every image.6 worked examples · 6 checks · Open explanation · member practiceMagnifiers, telescopes, microscopes and focal measurements →Trace the intermediate image, define the viewing condition and connect optical models to a bench experiment.9 worked examples · 8 checks · Open explanation · member practice

2. STAGE 2

   Compare optical paths

   Count optical path and reflection phase before adding amplitudes.

   Interference, diffraction and the structure of a fringe pattern →Turn path differences into phase, add fields and keep slit width distinct from slit separation.6 worked examples · 8 checks · Open explanation · member practiceInterference: phase, brightness and contrast →Predict what a detector reads by connecting path, phase and field addition.6 worked examples · 5 checks · Open explanation · member practiceThin films: reflections, colours and precision →Build a phase ledger, then use it for coatings, wedges and curved gaps.7 worked examples · 5 checks · Open explanation · member practice

3. STAGE 3

   Resolve and select light

   Separate grating spacing, slit width and illuminated width; then follow polarization through analysers.

   Gratings, spectra and resolving detail →Separate where a peak appears from how narrowly it can distinguish two signals.9 worked examples · 6 checks · Open explanation · member practicePolarization, analyzer chains and Brewster reflection →Project the electric field, keep an intensity ledger and identify the plane of incidence.6 worked examples · 7 checks · Open explanation · member practice

Choose a method before an equation

Use the physical conditions to narrow the choices. A formula becomes useful after you know why its model applies.

Try a complete free problem

These problems include the hints, worked reasoning and answer feedback. Attempt one before opening the solution.