Optics Study Guide

Level High SchoolReview time ~10 hours

Optics is geometry plus waves: rays bend at boundaries by Snell's law, lenses focus them by the lens equation, and wavelength explains the colors. Draw carefully, measure from the normal, and the subject is straightforward.

Key formulas

Lens Equation — 1/f = 1/do + 1/di

The reciprocals of image distance and object distance add up to the reciprocal of the focal length.

Power Formula — P = W/t

Power equals work done divided by the time taken.

Snell's Law — n₁sinθ₁ = n₂sinθ₂

The product of refractive index and sine of the angle is conserved across a boundary.

Wave Equation — v = fλ

Wave speed equals frequency times wavelength.

Topic checklist

Reflection

State the law of reflection: angle of incidence equals angle of reflection.
Draw ray diagrams with the normal line, not the surface, as reference.
Explain diffuse versus specular reflection.

Refraction and Snell's law

Apply Snell's law $n_1\sin\theta_1 = n_2\sin\theta_2$ with angles from the normal.
Predict bending toward or away from the normal using the index ratio.
Compute the critical angle for total internal reflection.

Mirrors and lenses

Locate images with the mirror/lens equation $1/f = 1/d_o + 1/d_i$ .
Use sign conventions consistently (real is positive for the standard convention).
Distinguish real images (projectable) from virtual ones.

Image formation and instruments

Explain how converging lenses focus parallel rays at the focal point.
Compute magnification $m = -d_i/d_o = h_i/h_o$ .
Describe how cameras, eyes, and microscopes form images.

Light as a wave

Connect wavelength to color: $v = f\lambda$ still rules light.
Explain dispersion: $n$ depends slightly on $\lambda$ .
Describe polarization as filtering one oscillation direction.

Interference and diffraction

Give the double-slit condition for bright fringes.
Explain why single-slit diffraction limits resolution.
Relate thin-film colors to path-difference interference.

Common mistakes

Mistake: Measuring angles from the surface instead of the normal.

Fix:

Snell's law, reflection, and the critical angle all measure from the normal (perpendicular), not the surface. Draw the normal first on every diagram — most sign and angle errors vanish with it.

Mistake: Calling every mirror image 'virtual' or 'real' without checking.

Fix:

Virtual images form where rays only appear to meet (behind mirrors, on the object's side of a magnifier) and cannot be projected. If you can catch it on a screen, it is real.

Mistake: Assuming all lenses make the same kind of image.

Fix:

Converging lenses and concave mirrors can make real or virtual images depending on object distance; diverging elements only make virtual ones. Run the equation instead of guessing from the shape.

Mistake: Confusing refraction with dispersion.

Fix:

Refraction needs an index change; dispersion needs the index to vary with wavelength. Glass does both at once, which is why prisms both bend and split light.

Mistake: Expecting interference from any two light sources.

Fix:

Interference needs coherent waves with a stable phase relationship — two independent light bulbs will not show fringes. Lasers and single slits earn their fringes through coherence.

Exam tips

Draw the normal line before any angle in reflection or refraction problems.
Write the sign convention you are using at the top of lens/mirror work.
For image questions, a quick ray diagram often answers faster than algebra.
In interference, convert path differences to multiples of $\lambda$ first.