Geometric and Physical Optics — AP Physics 2
1. Reflection and Snell's Law of Refraction ★★☆☆☆ ⏱ 5 min
When light hits a smooth opaque surface, it undergoes specular reflection that follows the law of reflection. All angles are always measured relative to the **normal**, an imaginary line perpendicular to the surface at the point of incidence.
When light passes between two transparent media with different optical densities, it changes speed and bends, a phenomenon called refraction. The refractive index $n$ quantifies how much a medium slows light:
n = \frac{c}{v}
where $c = 3\times10^8\ \text{m/s}$ is the speed of light in vacuum, and $v$ is the speed of light in the medium. The refractive index is always $n \geq 1$, with air approximated as $n=1.00$ for AP calculations. Snell's Law relates incident and refracted angles across two media:
n_1\sin\theta_1 = n_2\sin\theta_2
If $n_2 > n_1$, light bends toward the normal; if $n_2 < n_1$, light bends away from the normal.
Exam tip: Examiners often draw surfaces at oblique angles to trick you into measuring angles from the surface instead of the normal. Always draw the normal line explicitly before calculating angles.
2. Total Internal Reflection ★★☆☆☆ ⏱ 4 min
Total internal reflection (TIR) occurs when light travels from a higher-refractive-index medium to a lower-refractive-index medium, and the incident angle exceeds a threshold called the critical angle $\theta_c$. For angles above $\theta_c$, no refracted ray forms, and 100% of the light reflects back into the original medium.
The critical angle is defined as the incident angle where the refracted angle equals $90^\circ$. Substituting $\theta_2 = 90^\circ$ ($\sin 90^\circ = 1$) into Snell's Law gives the critical angle formula:
\sin\theta_c = \frac{n_2}{n_1}
TIR is the basis of fiber optic communication and prismatic binoculars, where it reduces energy loss and folds light paths to reduce device size.
3. Mirror and Lens Image Formation ★★★☆☆ ⏱ 6 min
All mirrors and lenses follow the same core equations, using the AP Physics 2 standard sign convention:
- Object distance $d_o$ is always positive for real objects (the default for all AP exam questions)
- Focal length $f$: positive for converging elements (concave mirrors, convex lenses), negative for diverging elements (convex mirrors, concave lenses)
- Image distance $d_i$: positive for real images (in front of mirrors, behind lenses), negative for virtual images (behind mirrors, in front of lenses)
- Magnification $m$: positive = upright image, negative = inverted image; $|m|>1$ = magnified, $|m|<1$ = reduced
The mirror/lens equation relates the three key quantities:
\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
The magnification formula relates image and object size and position:
m = -\frac{d_i}{d_o} = \frac{h_i}{h_o}
4. Diffraction and Interference ★★★☆☆ ⏱ 5 min
Diffraction is the bending of light around obstacles or through narrow openings, a phenomenon that can only be explained by the wave model of light. Huygens' Principle states that every point on a wavefront acts as a source of secondary spherical wavelets that spread out at the speed of light in the medium.
Interference occurs when two or more coherent light waves (same frequency, constant phase difference) overlap, following the principle of superposition:
- **Constructive interference**: Crests align with crests, producing a bright fringe. Occurs when path difference $\Delta r = m\lambda$, where $m = 0, \pm1, \pm2...$
- **Destructive interference**: Crests align with troughs, producing a dark fringe. Occurs when path difference $\Delta r = (m+\frac{1}{2})\lambda$
Coherence is required for a stable visible interference pattern; without it, fringes shift too rapidly to be observed.
5. Single-Slit and Double-Slit Patterns ★★★★☆ ⏱ 6 min
When monochromatic coherent light passes through two narrow, closely spaced slits (Young's double-slit experiment), diffracted light from each slit overlaps to form a pattern of equally spaced bright and dark fringes. The condition for bright fringes is:
d\sin\theta = m\lambda
For small angles ($\theta < 10^\circ$, the standard on AP exams), $\sin\theta \approx \tan\theta = \frac{y}{L}$, where $y$ is the distance from the central maximum to the fringe, and $L$ is the distance from the slits to the screen. The position of bright fringes becomes:
y = \frac{m\lambda L}{d}
The spacing between adjacent bright fringes is constant: $\Delta y = \frac{\lambda L}{d}$, where $d$ is the separation between the two slits.
When light passes through a single narrow slit, it produces a diffraction pattern with a wide, bright central maximum, and narrower, dimmer secondary maxima. The condition for dark fringes (minima) is:
a\sin\theta = m\lambda
where $a$ is the width of the single slit, and $m = \pm1, \pm2...$. Using the small angle approximation, the width of the central maximum (between $m=+1$ and $m=-1$ dark fringes) is $\frac{2\lambda L}{a}$.
Common Pitfalls
Why: Diagrams often draw surfaces at angles, making the surface easier to reference than the normal
Why: Students memorize the critical angle formula without remembering its context
Why: Convex lenses have positive $f$, but convex mirrors have negative $f$, leading to confusion
Why: Students mix up $a$ (single slit width) and $d$ (double slit separation), and forget the single-slit formula solves for dark fringes, not bright
Why: Students associate negative values with virtual properties