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Phys 2310 Mon. Sept. 12, 2015 Today’s Topics
• Continue Chapter 33: Geometric Optics • Reading for Next Time
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Chapter 5: Thin Lens Combinations • For lens combinations the object for the second lens is just the image
formed by the first. – Be careful about the sign of the object distance (see table 5.2)
• If d > s’1 then “object for the second lens is real. If d < s’1 then object is virtual. – See pgs. 167-169 in Hecht for equations and also the next slide.
• For the graphical method – You can solve lenses graphically by laying them out in a drawing program
(or even graph paper!) and tracing the Paraxial and Chief rays – Note that the “extra” ray (#9/10) goes through center of second lens. – In addition, ray #6/7 is deviated by second lens and must go through F’2 so
together they (#6/7 & # 9/10) locates the new image.
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Chapter 5: Thin Lens Combinations • Consider the second lens: • If d < s’1image is inverted, if d > s’1the image is upright (see figs. 5.28 and
5.30)
change)sign ofresult (note )'(
)'(s'
: then)'( nd-2 ofobject isst -1 of image since s'
used) are and Hecht in (note 11'1
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4
Chapter 33: Thin Len Combinations - II
• If the second lens is inside the focus of the first: – Convex lens
shortens the focal length (power is higher)
– Concave lens lengthens the focal length (power is negative)
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Chapter 33: Thin Len Combinations - III • Gaussian lens equation
can be applied to a sequence of lenses: just let the image of the first lens be the object of the second and so on. – Be Careful with Signs!
)()( b.f.l.
)()( f.f.l.
:becomen then combinatio for the lengths focal twoThe)/()/(
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#2) lens beyond is image theif negative becan this(Note :lens second for the Now
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6
Chapter 33: Thin Lens in Contact
• For lens in contact (separation is negligible) – Object distance of lens #2 = Image distance of lens
#1 • For an object at infinity:
power)each of sum is(power
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:or 111
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9
Chapter 33: Aperture Stops • Note that all lenses have finite diameters (aperture stop)
– Limits amount of light going through lens • It can larger or smaller than the lens aperture (see fig. 5.34, 5.35)
• Image plane also is finite (i.e., the detector): field stop – Limits size of image
• Internal stops in complex lens systems can help control the abberations of the lens Can also reduce illumination of the image plane as the off-axis angle increases (vignetting) – Useful for controlling stray light in infrared instruments
• We define the f#, or speed of a lens as f# = f/D – The smaller the number the brighter the image (and vice versa) – The smaller the f# the smaller the depth, or tolerance of focus
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Chapter 33: Mirrors - I
• Flat of Plane mirrors: – All images are virtual – Angle of reflection = angle of incidence – Object distance = image distance (fig. 5.40) – Virtual images of mirrors are reversed but
not inverted – Images from lenses are inverted but not
reversed – Used in laser scanners, some digital
projectors, and other instances where “beam steering” is needed
Chapter 33: Plane or Flat Mirrors
• Images with Plane Mirrors – Location of Virtual Image
Found by tracing rays from object.
– You see only those rays that enter your eye.
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Chapter 33: Mirrors - II • Spherical Mirrors:
– Images can also be formed by curved mirrors
– Concave mirrors form real images (f > 0)
– Convex mirrors form virtual images (f < 0)
• Focal length = 2 x Radius of Curvature
• Aspherical Mirrors: • From analytic geometry its clear the best axial image will be from a parabola not a sphere.
• Parabolic mirror is shape equal distance from incoming wavefront and a focus.
• However, off-axis images deteriorate rapidly.
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14
Example Problems
• Consider a bi-convex lens with R1 = R2 = 15cm. a) Determine the focal length of the lens b) Find the image distance for an object located 35cm from the
lens c) Make a ray diagram sketch for this configuration d) Make a sketch of the image distance vs. object distance
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Example Problems
• Consider a concave spherical mirror with fl = 60cm. a) Is the image real or virtual? b) Find the image of an object located 10.0 m away from the
mirror c) Make a ray diagram sketch for this configuration
• Repeat this example for a convex spherical mirror with fl = - 60cm