2: Geometrical Optics
- Page ID
- 128445
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 2.1: Rays, media, boundaries
- In media, and especially in condensed phases, EM radiation interacts with electrons and this slows the speed of light to less than c. At the interface between media, some light is transmitted and some reflected. Transmission and reflection depend on the material and also on wavelength.
- 2.2: Refraction, Snell's law.
- Slower wave speed implies shorter wavelength. From this and geometry, if follows that rays are refracted at interfaces, as given by Snell’s law of refraction: , where n is the refractive index. This explains lenses, mirages and much else.
- 2.3: Total internal reflection
- When has no solution, there is no refraction and there is total internal reflection with . Examples include optical fibres and cladding.
- 2.4: Dispersion
- In general, n is function of wavelength. So different colours refract differently, producing dispersion. This produces problems in lenses and some optical instruments. It also produces rainbows.
- 2.5: Mirrors and images
- Ray diagrams illustrate real and virtual images using parabolic and spherical mirrors. Focal length relates object and image distances, and magnification.
- 2.6: Lenses and images
- Lenses produce real and virtual images. Again, ray diagrams show how focal length relates object and image distances, and magnification.
- 2.7: Optical instruments
- We use lenses and ray diagrams to illustrate simple and compound microscopes and a refracting telescope, all of which exhibit chromatic aberration. We construct a reflecting telescope. Comparing ray optics and ray sonics, we make a long-range reflecting microphone.
- 2.8: Appendix
- 2.8.1: Snells law and refraction
- 2.8.2: Newton's prisms
- 2.8.3: Mirages and the Green Flash
- 2.8.4: Dispersion and chromatic aberration
- 2.8.5: Total internal reflection
- 2.8.6: Optical fibres and cladding
- 2.8.7: Chromatic dispersion, rainbows and Alexander's dark band
- 2.8.8: Colour of the sky
- 2.8.9: Mirrors and images
- 2.8.10: Lenses and images
- 2.8.11: Microscopes and magnifiers
- 2.8.12: Reflecting Newtonian telescope
- 2.8.13: Refracting telescope
- 2.8.14: Acoustic telescope
- 2.8.15: Geometrical Optics Experiments
- 2.9: Summary
- This page covers key concepts in optics and vision, highlighting electromagnetic waves, energy quantization, and diffraction. It examines the visible light spectrum, vision compared to other senses, and color mixing methods. The behavior of light through prisms and its dual nature in shadow formation are discussed. Additionally, it includes experiments such as Young's double-slit experiment and measurements of light speed, illustrating wave behavior principles.