Lecture 11 Geometric optics Physics 114 2242021 Lecture

Lecture 11 Geometric optics Physics 114 2/24/2021 Lecture XI 1

Principles of geometric optics 2/24/2021 Lecture XI 2

Concepts • • • Ray model of light Image formation Reflection Refraction Dispersion Total internal reflection 2/24/2021 Lecture XI 3

EM waves • c – speed of light (m/s) • f – frequency (Hz=1/s) • l – wavelength (m) 2/24/2021 Lecture XI 4

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!!! 2/24/2021 Lecture XI 5

Reflection • We see objects because – They emit light (Sun, light bulb) – They reflect light (Moon, table) • angle of incidence = angle of reflection: q i= q r 2/24/2021 Rough surface Lecture XI Polished surface. 6

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 2/24/2021 Lecture XI 7

Spherical mirrors • Convex mirror bulges out – diverges light • Concave mirror caves in – converges light 2/24/2021 Lecture XI 8

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 2/24/2021 Lecture XI 9

Ray tracing 3 Easy rays: 1. Parallel through focus 2. Through focus parallel (reversible rays) 3. Through the center of curvature C itself 2/24/2021 Lecture XI 10

Magnification • h 0 – object height – h 0>0 - always • hi – image height – hi>0 – upright image – hi<0 – inverted image • m=hi/h 0 - magnification 2/24/2021 |m|>1 –image larger than object |m|<1 –image smaller than object Lecture XI 11

Mirror equation • d 0 – distance to object – d 0>0 - always • di – distance to image – di>0 – real image – di<0 – virtual image 2/24/2021 Lecture XI 12

Convex mirror • Virtual focus – parallel beam focuses behind the mirror: f<0 • Same rules for ray tracing. 2/24/2021 Lecture XI 13

Sign convention for mirrors d 0>0 h 0>0 di>0 – real image hi>0 – upright image f>0 – concave mirror di<0 - virtual image hi<0 - inverted image f<0 – convex mirror • hi>0 di<0 – upright image is always virtual • hi<0 di>0 – inverted image is always real 2/24/2021 Lecture XI 14

Images in curved mirrors • • Concave mirror d 0>r – (real, inverted), smaller r>d 0>f – (real, inverted), larger d 0<f – (virtual, upright), larger 2/24/2021 Lecture XI • Convex mirror • Image is always (virtual, upright), smaller. 15

Speed of light in medium • Speed of light in vacuum: c=3. 0 x 108 m/s • Speed of light in media: v<c • Index of refraction: n=c/v >1. 0 2/24/2021 Lecture XI From table 33 -1 Vacuum n=1. 00 Air n=1. 0003 Water n=1. 33 Diamond n=2. 42 16

Refraction • The front is slowing down 2/24/2021 Lecture XI 17

Refraction, Snell’s law Bend toward normal Bend away from normal 2/24/2021 Lecture XI 18

Image formation • Eye still assumes light propagates in straight lines optical illusions – Image is shifted – Pool appears shallower 2/24/2021 Lecture XI 19

What if n depends on l? • If n depends on l angle of refraction depends on l • n(red)<n(green) 1. A-red, B-green 2. B- red, A-green A B Dispersion This is why rainbow occurs 2/24/2021 Lecture XI 20

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 2/24/2021 Lecture XI 21

1. 3 m 2. 1 m 2. 7 m x 2/24/2021 Lecture XI 22