PART VII KNOWLEDGE STRUCTURE
Optics

Key Findings

What are the overarching findings of Part VII?

Part VII has looked at two models of light: light waves and light rays.

Light waves
- Are electromagnetic waves.
- Spread out after passing through openings.
- Exhibit interference.

A third model of light, the photon model, will be introduced in Part VIII.

What laws of physics govern optics?

Superposition/interference

Constructive interference occurs where crests overlap crests, destructive interference where crests overlap troughs.

Law of reflection

$θ_{r} = θ_{i}$

Law of refraction (Snell’s law)

$n_{1} sin θ_{1} = n_{2} sin θ_{2}$

Rayleigh’s criterion

Two objects can be resolved by a lens of diameter $D$ if their angular separation exceeds $1.22 λ / D$ .

What are the most important models of Part VII?

Light is an electromagnetic wave.
- Light travels through vacuum at speed $c$ .
- Wavelength and frequency are related by $λ f = c$ .
Light exhibits diffraction and interference.
- Light spreads out after passing through an opening.
- Equal-wavelength light waves interfere. Interference depends on the path-length difference.
The wave model is usually appropriate for openings smaller than about 1 mm.

$The figure illustrates the interference pattern and diffraction pattern of light. The figure has two images one image on the top is diffraction and the interference is below it.$

Full Alternative Text

Light rays travel in straight lines.
- The speed is $v = c / n$ , where $n$ is the index of refraction.
Light rays travel forever unless they interact with matter.
- Reflection and refraction
- Scattering and absorption
An object is a source of rays.
- Rays originate at every point.
The eye sees by focusing a diverging bundle of rays.
The ray model is usually appropriate for openings larger than about 1 mm.

Full Alternative Text

What are the most important tools introduced in Part VII?

Bright equally spaced fringes are located at

$\begin{matrix} y_{m} = m L λ/ d & m = 0, 1, 2, \dots \end{matrix}$

Slit spacing $d$

Very narrow bright fringes are at

$\begin{matrix} d sin θ_{m} = m λ & y_{m} = L tan θ_{m} \end{matrix}$

If rays converge at $P'$ , then $P'$ is a real image and $s'$ is positive.
If rays diverge from $P'$ , then $P'$ is a virtual image and $s'$ is negative.

The thin-lens and thin-mirror equation for focal length $f$ is

$\frac{1}{s} + \frac{1}{s'} = \frac{1}{f}$
Lateral magnification is $m = - s' / s$ .

Hyperopia occurs when the eye’s near point is too far away. It is corrected with a converging lens.
Myopia occurs when the eye’s far point is too close. It is corrected with a diverging lens.

Diffraction limits optical instruments.
- The smallest spot to which light can be focused is $w_{min} = 2.44 λ f / D$ .
- Two objects can be resolved if their angular separation exceeds $1.22 λ / D$ .
  
  $A photograph of an overlapping diffraction pattern.$