PRACTICE COLLECTION / 47 PROBLEMS
Optics
Trace rays and turn path differences into fringes. Each problem includes progressive hints, guided reasoning and a question to test the idea again. Problems marked “Free sample” are complete for everyone; membership opens the rest.
LEARN BEFORE YOU PRACTISE
Build the reasoning first.
From changing electric fields to electromagnetic waves
Resolve the capacitor-gap puzzle, derive the wave speed and follow energy through the fields.
7 worked examples · 8 checks →Refraction, internal reflection and dispersion
Draw the normal, trace each boundary and let the geometry decide which formula applies.
9 worked examples · 7 checks →Images 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 →Spherical 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 →Magnifiers, 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 →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 →Interference: phase, brightness and contrast
Predict what a detector reads by connecting path, phase and field addition.
6 worked examples · 5 checks →Thin films: reflections, colours and precision
Build a phase ledger, then use it for coatings, wedges and curved gaps.
7 worked examples · 5 checks →Gratings, spectra and resolving detail
Separate where a peak appears from how narrowly it can distinguish two signals.
8 worked examples · 5 checks →Polarization, analyzer chains and Brewster reflection
Project the electric field, keep an intensity ledger and identify the plane of incidence.
6 worked examples · 7 checks →CONCEPTS IN THIS COLLECTION
PRACTISE AT YOUR PACE
Problems in this collection
47 problems · Showing 12
Optics
Changing medium does not rename the source frequency
What is its wavelength inside the material?
Compare casesOptics
Build the refracted angle from wavefront timing
What is sin of the refracted angle to the normal?
Connect conceptsOptics
Removing a beam can brighten one point
Interference can make removing one field increase the local intensity.
Compare casesOptics
Infer two beams from their brightest and dimmest readings
What is the ratio of the stronger beam intensity to the weaker one?
Read graphs & measurementsOptics
One intensity does not identify which wave leads
What is that phase lag?
Find a missing quantityOptics
Count only the optical path a plate adds
What is the new combined intensity?
Connect conceptsOptics
The substrate changes which thickness reinforces reflection
What is the smallest positive film thickness for a reflected phase maximum?
Apply a principleOptics
Measure index without knowing the fringe order
What film refractive index follows from the spacing?
Read graphs & measurementsOptics
Turn fringe spacing into a physical gap
What is the gap thickness at the raised edge?
Connect conceptsOptics
Masking changes sharpness, not centre separation
What is the ratio of the angular separation of the line centres after masking to before masking?
Compare casesOptics
A flat screen needs tangent geometry
How far from the central maximum is the first-order maximum on the screen?
Connect conceptsOptics
Design for an angular separation before choosing magnification
What minimum aperture diameter meets the ideal Rayleigh criterion?
Find a missing quantity12 of 47 shown