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Lenses Physics 202 Professor Lee Carkner Lecture 21

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Refraction Lenses have focal lengths and real and virtual images, but their properties also depend on the index of refraction It has two sides we have to account for thin symmetric lenses two identical refracting surfaces placed back to back

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Lenses and Mirrors Mirrors produce virtual images on the opposite side from the object i is negative in both cases Mirrors produce real images on the same side as the object i is positive in both cases If a mirror curves towards the object, f and r are positive (real focus) Real is positive, virtual is negative

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Converging Lens Rays initially parallel to the central axis are focused to the focal point after refraction The focal point is on the opposite side from the incoming rays Converging lenses produce images larger than the object m = -i/p

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Diverging Lens Rays initially parallel to the central axis diverge after refraction, but can be traced back to a virtual focus f is virtual and negative Diverging lenses produce images smaller than the object

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Lens Equations A thin lens follows the same equation as a mirror, namely: 1/f = 1/p + 1/i 1/f = (n-1) (1/r 1 -1/r 2 ) Where r 1 and r 2 are the radii of curvature of each side of the lens (r 1 is the side nearest the object) For symmetric lenses r 1 and r 2 have opposite sign

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Converging Lenses and Images Objects in front of the focal point (nearer to the lens) produce virtual images on the same side as the object Image is virtual so i is negative Objects behind the focal point (further from the lens) produce real images on the opposite side of the lens Image is real so i is positive

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Diverging Lenses and Images For either lens the location of images is the reverse of that for mirrors: Real images have positive i, virtual images have negative i

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1)

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2)

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Two Lenses To find the final image we find the image produced by the first lens and use that as the object for the second lens M = m 1 m 2 We can approximate several common optical instruments as being composed of a simple arrangement of thin lenses In reality the lenses are not thin and may be arranged in a complex fashion

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Dual Lenses

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Near Point How can you make an object look bigger Increases angular size The largest clear (unlensed) image of an object is obtained when it is at the near point (about 25 cm) A converging lens will increase the angular diameter of an object m = ’/

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Magnifying Lens If the object is inside the near point you can view it through a lens which will produce a virtual image outside of the near point The magnification is: m = 25 cm /f This is the size of the object seen through the lens compared to its size at the near point

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Magnifying Glass

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Compound Microscope The objective creates a real image focused at the focal point of the eyepiece The magnification of the objective is m = -i/p i is very close to the distance between the lenses, s The total magnification is the product of the magnification of each M = (-s/f ob )(25 cm/f ey ) where s is the distance between the focal point of the lenses (the tube length) and f is the focal length

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Microscope

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Refracting Telescope The rays coming in from infinity are refracted by the objective to create a real image at the common focal point The total angular magnification of the telescope depends on the ratio of the eyepieces m = -f ob /f ey

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Refracting Telescope

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Newtonian Telescope

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Telescopes The magnification of the telescope can be altered by changing eyepieces Short focal length means more magnification Limited by blurring effects of atmosphere The largest practical refracting telescope has an objective with a diameter of about 1m The objective becomes so large it is hard to build and support

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Next Time Read: 35.1-35.5

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For a plane mirror what is the sign of f, the type of image and the orientation of the image? A)+, real, upright B)+, virtual, upright C)-, virtual, inverted D)No sign, virtual, upright E)No sign, real, inverted

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For a convex mirror what is the sign of f, the type of image and the orientation of the image? A)+, real, upright B)+, virtual, upright C)-, virtual, inverted D)-, virtual, upright E)+ real, inverted

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For a concave mirror (with object close to the mirror) what is the sign of f, the type of image and the orientation of the image? A)+, real, upright B)+, virtual, upright C)-, virtual, inverted D)-, virtual, upright E)+, real, inverted

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For a concave mirror (with object far from the mirror) what is the sign of f, the type of image and the orientation of the image? A)+, real, upright B)+, virtual, upright C)-, virtual, inverted D)-, virtual, upright E)+, real, inverted

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