Lecture 11 Geometric optics Physics 114 12/8/2018 Lecture XI

Principles of geometric optics 12/8/2018 Lecture XI

Concepts Ray model of light Image formation Reflection Refraction Dispersion Total internal reflection 12/8/2018 Lecture XI

EM waves c – speed of light (m/s) f – frequency (Hz=1/s) l – wavelength (m) 12/8/2018 Lecture XI

Ray model of light Light is an EM wave diffraction (go around obstacles) This happens on microscopic scale In everyday life we use straight line approximation for light propagation = Ray model of light  geometric optics We infer positions of objects assuming light travels in straight lines. Geometry is important, Bring ruler and pencil, make good pictures!!! 12/8/2018 Lecture XI

Reflection We see objects because They emit light (Sun, light bulb) They reflect light (Moon, table) angle of incidence = angle of reflection: qi=qr Rough surface Polished surface. 12/8/2018 Lecture XI

Formation of image Eye assumes light propagates in straight lines  image (rays of light crossing) is formed behind the mirror do – distance to object di – distance to image For plane mirror do= di No light here  Virtual image If light actually goes through the place where image is formed  real image 12/8/2018 Lecture XI

Spherical mirrors Convex mirror bulges out – diverges light Concave mirror caves in – converges light 12/8/2018 Lecture XI

Focus Parallel beam of light (e.g. from a very distant object) is converged in 1 point – focal point F Distance from the mirror to F is called focal distance, or focus f =r/2 12/8/2018 Lecture XI

Ray tracing 3 Easy rays: Parallel  through focus Through focus  parallel (reversible rays) Through the center of curvature C  itself 12/8/2018 Lecture XI

Magnification h0 – object height hi – image height h0>0 - always hi – image height hi>0 – upright image hi<0 – inverted image m=hi/h0 - magnification |m|>1 –image larger than object |m|<1 –image smaller than object 12/8/2018 Lecture XI

Mirror equation d0 – distance to object di – distance to image d0>0 - always di – distance to image di>0 – real image di<0 – virtual image 12/8/2018 Lecture XI

Convex mirror Virtual focus – parallel beam focuses behind the mirror: Same rules for ray tracing. 12/8/2018 Lecture XI

Sign convention for mirrors d0>0 h0>0 di>0 – real image di<0 - virtual image hi>0 – upright image hi<0 - inverted image f>0 – concave mirror f<0 – convex mirror hi>0di<0 – upright image is always virtual hi<0di>0 – inverted image is always real 12/8/2018 Lecture XI

Images in curved mirrors Concave mirror d0>r – (real, inverted), smaller r>d0>f – (real, inverted), larger d0<f – (virtual, upright), larger Convex mirror Image is always (virtual, upright), smaller. 12/8/2018 Lecture XI

Speed of light in medium Speed of light in vacuum: c=3.0x108m/s Speed of light in media: v<c Index of refraction: n=c/v >1.0 From table 33-1 Vacuum n=1.00 Air n=1.0003 Water n=1.33 Diamond n=2.42 12/8/2018 Lecture XI

Refraction The front is slowing down 12/8/2018 Lecture XI

Refraction, Snell’s law Bend toward normal Bend away from normal 12/8/2018 Lecture XI

Image formation Eye still assumes light propagates in straight lines  optical illusions Image is shifted Pool appears shallower 12/8/2018 Lecture XI

What if n depends on l? If n depends on l  angle of refraction depends on l n(red)<n(green) A-red, B-green B- red, A-green A B Dispersion This is why rainbow occurs 12/8/2018 Lecture XI

Total internal reflection For q>qc - total internal reflection – no light come out – all light is reflected Fiber optics Necessary condition: from thick to thin media 12/8/2018 Lecture XI

1.3 m 2.1 m 2.7 m x 12/8/2018 Lecture XI