Optics Fundamentals
Optics Fundamentals
This domain tests whether you can move between ray, wave, and photon descriptions of light and apply first principles without hidden assumptions. Expect Snell's law, thin-lens imaging, Gaussian beams, two-beam interference, diffraction, and polarization.
Core rules
- Refraction: (n_1\sin\theta_1=n_2\sin\theta_2), with angles from the surface normal.
- Thin lens: (1/f=1/s+1/s'), transverse magnification (m=-s'/s) under the real-is-positive convention.
- Interference depends on optical path difference, not geometric path alone; coherence limits visible fringes.
- Diffraction sets a finite resolution scale; polarization states are combined as vectors, not scalars.
Worked example
An object sits 100 mm from a converging lens of focal length 25 mm. Find the image distance and magnification. Using (1/25=1/100+1/s'), (1/s'=1/25-1/100=3/100), so (s'=33.3) mm. Then (m=-33.3/100=-0.333): the image is real, inverted, and one-third size. A 10 mm object becomes 3.33 mm tall.
Traps
Mixing sign conventions is the most common error. Refractive index must be stated at a wavelength; using a catalog value at the wrong wavelength shifts dispersion calculations. Small-angle approximations fail near grazing incidence. In interference, a phase reversal on reflection can add (\pi), changing bright to dark. Do not treat coherence length as equal to wavelength.
Exam focus
Be ready to estimate orders of magnitude and check units: radians versus degrees, millimetres versus metres, and power versus energy.