# Image1 - Image Formation in Man and Machines Image...

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Image formation - 1 Image Formation in Man and Machines

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Image formation - 2 Overview v Pinhole camera v Refraction of light v Thin-lens equation v Optical power and accommodation v Image irradiance and scene radiance v Human eye v Geometry of perspective imaging
Image formation - 3 Lens-less Imaging Systems - Pinhole Optics v Pinhole optics projects images without lens with infinite depth of field v Smaller the pinhole better the focus less the light energy from any single point v Good for tracking solar eclipses Pinhole Image Scene Blurred Image

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Image formation - 4 Diffraction v Two disadvantages to pinhole systems Low light collecting power diffraction v Diffraction Light bends as it passes by the edge of a narrow aperture v Human vision at high light levels, pupil (aperture) is small and blurring is due to diffraction at low light levels, pupil is open and blurring is due to lens imperfections D λ θ= D
Image formation - 5 Diffraction and pinhole optics

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Image formation - 6 Lenses Collect More Light v With a lens, diverging rays from a scene point are converged back to an image point Center of projection Image plane Scene Lens
Image formation - 7 incident ray reflected ray refracted ray refracted ray v If θ is the angle of incidence and θ is the angle of refraction then where n and n are the refractive indices of the two media v Refractive index is the ratio of speed of light in a vacuum to speed of light in the medium Refraction: Snell’s law Refractive indices glass - 1.50 water - 1.333 air - 1.000 θ ' sin ' sin θ θ n n =

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Image formation - 8 Lens Equations
Image formation - 9 Thin-Lens Equation v Thin-lens equation relates the distance between the scene point being viewed and the lens to the distance between the lens and the point’s image (where the rays from that point are brought into focus by the lens) Let M be a point being viewed u p is the distance of M from the lens along the optical axis u The thin lens focuses all the rays from M onto the same point, the image point m at distance q from the lens. M O F m f q-f pq H h Q S s

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Image formation - 10 Thin-Lens Equation v m can be determined by intersecting two known rays MQ is parallel to the optical axis, so it must be refracted to pass through F. MO passes through the lens center, so it is not bent. v Note two pairs of similar triangles MSO and Osm (yellow) OQF and Fsm (green) f q p 1 1 1 = + q p h H q h p H + + = = q h H f q h f H + = = q q p f p + = M O F m f q -f pq H h Q S s q p q p f + = 1 Divide 2 equations:
Image formation - 11 Thin-Lens Equation v Notice that the distance behind the lens, q , at which a point, M , is brought into focus depends on p , the distance of that point from the lens familiar to us from rotating the focus ring of any camera f q p 1 1 1 = + M O F m f q-f pq H h Q S s

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Image formation - 12 Thin-Lens Equation v As p gets large, q approaches f v As q approaches f , p approaches infinity f q p 1 1 1 = + M O F m f pq Q S M’ S’ m’
Image formation - 13 Optical Power and Accommodation v

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## Image1 - Image Formation in Man and Machines Image...

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