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Unformatted text preview: Image formation by lenses Image Formation 5.2 Image formation by lenses Convex lenses Concave lenses • Images can be formed by lenses that divert light rays by refraction. • Convex, converging lenses form real images and virtual images like concave mirrors. • Concave, diverging lenses only form virtual images, like convex mirrors. • We discuss the ideal case of thin lenses, i.e. paraxial rays. Real lenses show distortions due to spherical aberration and chromatic aberration. Convex and Concave Lenses Convex – Converging Lens Lensmaker’s equation convention on radii R R is positive R is negative. Concave – Diverging Lens thin lens in air (d<<R , R ) 1 2 æ 1 1 1 ö = (n - 1) ç ÷ f è R1 R 2 ø Question A double convex lens is made out of glass with a refractive index of 1.75. If the radius of curvature of the two surfaces were the same what radius would give a lens with a focal length of f=25 cm? Convex, Converging Lens A convex lens converges parallel rays onto a focal point, f. 1 Focusing by a converging lens Ray tracing for lenses • A line parallel to the lens axis passes through the focal point • A line through the center of the lens passes through undeflected. f Images formed by a converging lens converging light Real Inverted reduced Image formed by a converging lens converging light Real Inverted Enlarged diverging light Virtual Upright Enlarged http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html Question How will an object viewed through a converging lens appear as the lens is brought closer to the object? 2 Diverging lens Diverging parallel rays trace back to the focal point. The light does not actually pass through the focal point. You can’t make a fire focusing sunlight with a diverging lens. Image formed by a diverging lens Image formed by a diverging lens http://micro.magnet.fsu.edu/primer/java/lenses/diverginglenses/index.html Virtual Upright Reduced 3 Question How will the image of an object formed by a diverging lens change as the lens is brought closer to the object? Thin Lens Equation Magnification 1 1 1 + = l l ' f
f is positive for converging lens, f is negative for a diverging lens. m = h ' l ' =h l Negative m for an inverted image Positive m for an upright image 4 Question A converging lens with a focal length of 10 cm is placed 30 cm in front of a candle. Find the image distance. Find the magnification. Question A candle and a screen are 70 cm apart. Find two points between the candle and screen where you could put a convex lens with a 17 cm focal length to give a sharp image of the candle on the screen. Find the magnification at the two positions. f Projector lens Camera Suppose you want to project the image of a transparency 35 mm high on to a screen that is 1.5 m high using a lens with a focal length of 10 cm. Where would you position the film? How far from the lens would you place the screen? . The camera is the inverse of the projector. The image and object are reversed Spherical Aberration Chromatic Aberration nonparaxial rays paraxial rays 5 Fresnel Lens 6 ...
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