Ray Optics Ray model Reflection Refraction total internal reflection Color dispersion Lenses Image formation Magnification Spherical mirrors 1 Ray optics Optical imaging and color in medicine Integral part of diagnosis 2 Ray model Ray model is composed of light rays abstract idea to show the direction along which light energy flows Works for systems where the objects are much larger than the wavelength of light 3 Ray model rules Light travels in straight lines Light rays can cross 4 Ray model rules Light rays travel though materials with a speed c n where n is the refractive index At a boundary light can be reflected or refracted or both Within a material light can be scattered or absorbed 5 Ray model rules Light rays originate from objects The object radiates in all directions The light may be from the object self luminous objects light bulbs or the light may be reflected 6 Ray model rules Light rays are detected by the eye if they pass through the pupil and can be focused onto the retina at the back of the eye 7 Seeing Objects Objects are seen when light scattered or transmitted from an object enters the eye 8 Shadows Light rays can be absorbed by an opaque object For an extended source shadows can be fuzzy 9 Pin hole camera The pin hole camera selects rays which will create an inverted image 10 Pin hole camera Advantages no focusing required infinite field of depth no color dispersion Disadvantage requires long exposure time 11 Reflection specular reflection is the reflection from a flat surface 12 Reflection diffuse reflection is the reflection from a flat surface 13 Plane Mirror Images The reflected image in a mirror is virtual A screen placed there would not show an image 14 Plane Mirror Images The reflected image in a mirror is not inverted The correct terminology for a reflected image is to say it reverses front and back Or say the image is reflected 15 Refraction Light rays get bent going through a medium boundary 16 Snell s law Snell s law relates the angle of refraction to the index of refraction n1 sin 1 n2 sin 2 17 Snell s Law The frequency of the light must be a constant The length of the wave front at the boundary must be a constant 1 2 l sin 1 sin 2 v c f nf c c l n1 f sin 1 n2 f sin 2 18 Snell s law Snell s law is a consequence of light slowing down in a medium Works in either direction Independent of reflections n1 sin 1 n2 sin 2 19 Total Internal Reflection When light is leaving a denser medium to go into a lighter medium above a certain angle Snell s law predicts unreal angles sin 1 This angle is the critical angle Above this angle light will not be refracted it undergoes total internal reflection TIR 20 Total Internal Reflection The critical angle for the boundary between two media can be calculated as n1 sin c n2 sin 90 o n2 c sin n1 n2 n1 1 21 TIR application Used in fiber optics The fiber has a core 8 m or 50 62 5 m surrounded by cladding 125 m ncore ncladding 22 Color Color is a property of the human eye The eye detects different wavelengths as different photo chemical reactions White light is a mixture of all colors The refractive index of materials changes slightly with color 23 Color Dispersion The refractive index of materials changes slightly with color and a prism can be used to split up and recombine the different colors in white light 24 Color Dispersion Rainbows are created by color dispersion in water droplets in the sky 25 Color Dispersion Rainbows are created by color dispersion in water droplets in the sky 26 Colored Objects Objects have a color because they either transmit light e g colored glass or reflect light e g leaves An object which transmits red light is absorbing all colors other than red An object which reflects green light is absorbing all colors other than green 27 Questions Q What colors are absorbed by blue glass A Q What color is absorbed by black paper A Q What color is absorbed by white paper A Q What color will a green apple seen through red glass be A 28 Questions Q What colors are absorbed by blue glass A All except blue Q What color is absorbed by black paper A All colors Q What color is absorbed by white paper A No colors Q What color will a green apple seen through red glass be A black 29 Images from Refraction Images in water either a tank or viewed through an underwater face mask appear larger and closer 30 Images from Refraction Rays from the object are refracted when they meet the water air boundary We can calculate the apparent distance s from the edge of the tank or face mask 31 Images from Refraction The ratio of the actual and apparent distances from the boundary is related to the ratio of the tangents l s tan 1 s tan 2 tan 1 s s tan 2 32 Images from Refraction Using the small angle approximation and Snell s Law we find the position of the image tan 1 sin 1 s s s tan 2 sin 2 n2 s s n1 1 33 Lenses A lens focuses light rays by refraction In a converging lens parallel rays converge to a single point called the focal point The surfaces are ground to be spherical 34 Converging and Diverging Lenses Two types of lenses Converging lens thicker in the middle light rays refract towards the optical axis Diverging lens thinner in the middle light rays refract away from the optical axis The focal point is the point from which paraxial rays converge or diverge 35 Converging Lenses The focal length is the distance from the lens at which rays parallel to the optical axis converge These rays are known as paraxial rays 36 Converging Lenses Similarly the focal length is the distance from the lens at which rays will refract out of the lens parallel to the optical axis 37 Converging Lenses Light through the center of the lens pass through without changing angle These rays are known as principal rays 38 Real Images A real image can be seen in focus on a screen Note they are always inverted with a simple converging lens when s f 39 Real Images Another definition for a real image is that the rays converge at a point at the image plane 40 Virtual Images For a virtual image the rays diverge from a point in the object plane 41 Pin hole Images Rays for pin hole images neither diverge nor converge although they do project onto a screen Sometimes called a projected image 42 In focus images The image will only be in focus at the particular plane where rays from the same point on the object converge The image will appear blurry if the screen is not at the image plane 43 Finding images The …
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