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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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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.

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#2) lens beyond is image theif negative becan this(Note :lens second for the Now

or, 111:LensFirst For the

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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

111

:or 111

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Chapter 33: Image Properties - I

Sign Conventions (very important, memorize!)

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Chapter 33: Image Properties

Convex vs. Concave Lenses

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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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Chapter 33: Sign Conventions

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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

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Reading this Week By Wednesday:

Finish Ch. 33 Lenses and Prisms Begin Ch. 34 Optical Systems