19 Optics 4 - Lensmaker formula C onverging lenses are...

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Unformatted text preview: Lensmaker formula C onverging lenses are thickest in the middle and have positive focal lengths Diverging lenses are thickest at the edges and have negative focal lengths = 2 1 1 1 ) 1 ( 1 R R n f Equation for focal length of a lens 1 > R 2 < R 1 < R 2 > R Biconvex lens + = 2 1 1 1 ) 1 ( 1 R R n f Biconcave lens = 2 1 1 1 ) 1 ( 1 R R n f Lensmaker formula = 2 1 1 1 ) 1 ( 1 R R n f Made of glass (n = 1.52) and bi-convex with R 1 = 10 cm and R 2 = 6 cm 1 > R 2 < R 1 < R 2 > R 1 m 86 . 13 m 06 . 1 m 1 . 1 ) 1 52 . 1 ( 1 = + = f cm 2 . 7 = f Lens aberrations, spherical: Ideally, the surface of a lens should be parabolicE Those are very difficult to make, though! Spherical shape is rather close to a parabola for paraxial rays, which are close to the axis of the lens. The rays, which come at greater angles (further away from the axis) converge in a different, closer point. The image of the point O gets blurryE Lens aberrations, chromatic: Regular glass materials are dispersive: indices of refraction are different for different colors. Rays of different colors are refracted through different angles and converge in different points the image gets blurry! Remedies try to use a single color illumination or a composite lens compensating for the dispersion. High end microscope objective collect light from wide angles and compensate for all possible aberrationsE 1 , / ' ; 2 ' and ' , 2 , < < = < > > > M l l M f l l f l f Real, inverted, reduced f l l 1 ' 1 1 = + f l l 1 , / ' ; 2 ' and ' , 2 , > < = > > < < > M l l M f l l f l f f Real, inverted, magnified l l f F F f l l 1 ' 1 1 = + 1 , / ' ; ' and ' , , > > = > < < > M l l M f l l f l f Virtual, upright, magnified f l l A camera....
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19 Optics 4 - Lensmaker formula C onverging lenses are...

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