Geometric and Physical Optics
Optics is one of the most reliably tested physics areas on the MCAT, and it rewards a firm grasp of a handful of equations plus sign conventions. The AAMC content outline expects you to handle reflection and refraction, mirrors and lenses, total internal reflection, the optics of the human eye, and physical optics (interference, diffraction, polarization). This is a high-yield topic on the MCAT.
Nature of Light
Light is an electromagnetic wave that travels in a vacuum at c = 3 × 108 m/s. Like all waves it obeys c = fλ. Visible light spans roughly 400 nm (violet) to 700 nm (red). Light exhibits both wave behavior (interference, diffraction) and particle behavior (photons, E = hf) — the wave picture governs the optics tested here.
When light enters a medium its speed drops to v = c/n, where n is the refractive index. Frequency stays constant across a boundary; wavelength changes (λmedium = λvacuum/n).
Reflection and Mirrors
Law of reflection: the angle of incidence equals the angle of reflection (both measured from the normal), θi = θr.
- Plane mirror: forms a virtual, upright, same-size image as far behind the mirror as the object is in front (m = +1).
- Concave (converging) mirror: can form real, inverted images (object beyond f) or virtual, magnified, upright images (object inside f) — the shaving/makeup mirror.
- Convex (diverging) mirror: always forms a virtual, upright, reduced image — the passenger-side/security mirror with a wide field of view.
Mirror and lens equation
The same thin-optics equation governs both mirrors and lenses:
1/f = 1/do + 1/di and m = −di/do = hi/ho
For a spherical mirror the focal length is half the radius of curvature: f = R/2.
| Quantity | Positive (+) | Negative (−) |
|---|---|---|
| Focal length f | Converging (concave mirror, convex lens) | Diverging (convex mirror, concave lens) |
| Image distance di | Real image (mirror: same side as object; lens: opposite side) | Virtual image |
| Magnification m | Upright image | Inverted image |
| |m| | > 1 enlarged | < 1 reduced |
Refraction and Snell's Law
When light crosses into a medium of different index it bends. Snell's law:
n1 sinθ1 = n2 sinθ2
Light entering a denser medium (higher n) bends toward the normal and slows down; entering a rarer medium it bends away from the normal. The index n = c/v ≥ 1 (nvacuum = 1, nair ≈ 1.0, nwater ≈ 1.33, nglass ≈ 1.5).
Total internal reflection
When light travels from a denser to a rarer medium, at a large enough incidence angle it reflects entirely back — total internal reflection (TIR). It occurs only when n1 > n2 and θ > the critical angle:
sinθc = n2/n1
TIR is the principle behind fiber optics (including medical endoscopes) and the sparkle of diamond (very high n ⇒ small θc).
Dispersion
Because n depends slightly on wavelength, a prism separates white light into colors — dispersion. Violet (shorter λ) bends most; red (longer λ) bends least. This is also the mechanism behind rainbows.
Lenses and Lens Power
Converging (convex) lenses have f > 0 and can form real or virtual images; diverging (concave) lenses have f < 0 and only form virtual, upright, reduced images. The same equation 1/f = 1/do + 1/di applies.
The power of a lens is the reciprocal of its focal length in meters, measured in diopters (D):
P = 1/f (f in meters, P in diopters)
For lenses in contact (e.g., a corrective lens near the eye), powers add: Ptotal = P1 + P2. Converging lenses have positive power; diverging lenses have negative power.
Optics of the Human Eye
The eye is the MCAT's favorite applied-optics system. The cornea and lens together form a real, inverted image on the retina. The lens changes shape (accommodation) to focus objects at different distances.
| Condition | Problem | Image forms | Corrective lens |
|---|---|---|---|
| Myopia (nearsighted) | Eye too long / too much converging power | In front of retina | Diverging (concave, − power) |
| Hyperopia (farsighted) | Eye too short / too little converging power | Behind retina | Converging (convex, + power) |
| Presbyopia | Age-related loss of accommodation | Cannot focus near objects | Converging (reading glasses) |
| Astigmatism | Non-spherical cornea | Blurred/distorted | Cylindrical lens |
Physical Optics: Interference and Diffraction
Physical (wave) optics covers phenomena that only the wave model explains.
- Interference. Coherent waves superpose: constructive when the path difference is a whole number of wavelengths (mλ), destructive when it is a half-integer number ((m + ½)λ).
- Young's double slit. Produces bright/dark fringes with spacing Δy = λL/d (L = slit-to-screen distance, d = slit separation). Longer wavelength or wider L ⇒ wider fringes; larger d ⇒ narrower fringes.
- Thin-film interference. Colors in soap bubbles and oil slicks, and anti-reflective coatings on lenses. Remember the λ/2 phase shift on reflection off a higher-index medium.
- Diffraction. Waves bend around obstacles and spread through apertures; most pronounced when the opening is comparable to λ. A diffraction grating sharpens the fringes used to measure wavelengths.
- Polarization. Light is a transverse wave, so it can be polarized (filtered to one plane of oscillation). Polarizing sunglasses cut glare (reflected light is partially polarized). Sound, being longitudinal, cannot be polarized — a favorite MCAT contrast.
Worked MCQs
Five MCQs that capture the high-yield testing patterns for this chapter.
Q1. An object is placed 30 cm in front of a converging lens of focal length 10 cm. Where is the image?
1/di = 1/f − 1/do = 1/10 − 1/30 = (3 − 1)/30 = 2/30, so di = 15 cm. Positive di means a real image on the opposite side of the lens.
Q2. For that same lens and object, the magnification is:
m = −di/do = −15/30 = −0.5. The negative sign means inverted; |m| < 1 means reduced to half height.
Q3. Light passes from glass (n = 1.5) toward air (n = 1.0). The critical angle for total internal reflection is closest to:
sinθc = n2/n1 = 1.0/1.5 = 0.667, so θc = sin−1(0.667) ≈ 42°. TIR requires going from the denser to the rarer medium, which is satisfied here.
Q4. A person is nearsighted (myopic). The correcting lens should be:
In myopia the image forms in front of the retina because the eye over-converges. A diverging (concave, negative-power) lens spreads the rays first so the image lands on the retina.
Q5. In a Young's double-slit experiment, the spacing between bright fringes on the screen will increase if you:
Fringe spacing Δy = λL/d. It grows with wavelength λ and screen distance L, and shrinks with slit separation d. Higher frequency means shorter λ (narrower fringes), so the only option that widens the fringes is longer wavelength.
Quick Recap
- Reflection: θi = θr; plane mirror gives a virtual, upright, same-size image.
- Mirror/lens equation: 1/f = 1/do + 1/di; m = −di/do; mirror f = R/2.
- Sign convention: real image di > 0 (inverted); virtual image di < 0 (upright).
- Snell's law: n1 sinθ1 = n2 sinθ2; n = c/v.
- Total internal reflection: sinθc = n2/n1, only from dense to rare medium.
- Lens power P = 1/f in diopters; converging + , diverging − ; powers add in contact.
- Eye: myopia → diverging lens; hyperopia → converging lens.
- Physical optics: double-slit Δy = λL/d; light can be polarized, sound cannot.