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Announcements •  HW set 9 due this week; covers Ch 23 and Ch 24.1-4 •  Office hours:

• Prof Kumar’s Tea and Cookies 5 – 6 pm today • My office hours Th 2 -3 pm

•  or make an appointment

•  Come to class April 19 •  course and instructor evaluation •  8 bonus HITT points

•  Always check out http://www.phys.ufl.edu/courses/phy2054/spring11/ for more announcements

QUESTIONS? PLEASE ASK!

Review

n  Mirrors n  Definitions, Types n  Magnification

n  Mirror equation

n  Remember the sign conventions! (Table 23.1)

n  Ray tracing n  Images formed by

refraction n  Magnification

n  Object-Image

M =h 'h

= !qp

1p+1q=2R=1f

Concave

Convex

M =h 'h

= !n1qn2p

n1

p+n2

q=n2! n

1

R

Atmospheric Refraction and Mirages n  A mirage can be observed

when the air above the ground is warmer than the air at higher elevations

n  The rays in path B are directed toward the ground and then bent by refraction

n  Related to total internal reflection – n is smaller near the ground

n  The observer sees both an

upright and an inverted image

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Thin Lenses

n  Thin lens - consists of a piece of glass or plastic n  refracting surfaces are either

spherical or planar n  distance between the surface of the

lens and the center of the lens is negligible

n  converging lenses n  positive focal lengths n  thickest in the middle

n  diverging lenses n  negative focal lengths n  thickest at the edges

Converging lenses

Diverging lenses

Focal Length of Lenses n  focal length, ƒ -image distance that

corresponds to an infinite object distance n  same as mirrors n  thin lens has two focal points, corresponding to

parallel rays from the left and from the right

Converging lenses Diverging lenses

Lens Equations n  The geometric derivation of the

equations is very similar to that of mirrors

M =h 'h

= !qp

1p+1q=1f

§ The equations can be used for both converging and diverging lenses

§  converging lens has a positive focal length §  diverging lens has a negative focal length

Focal Length for a Lens n  The focal length of a lens is related to the curvature of its

front and back surfaces and the index of refraction of the material

the lens maker’s equation

1f= (n !1) 1

R1

!1R2

"

#$$

%

&''

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Ray Diagrams for Thin Lenses

n  Three rays are drawn n  The first ray is drawn parallel to the first

principle axis and then passes through (or appears to come from) one of the focal lengths

n  The second ray is drawn through the center of the lens and continues in a straight line

n  The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis

n  There are an infinite number of rays, these are convenient

Ray Diagram for Converging Lens, p > f

n  The image is real n  The image is inverted

Ray Diagram for Converging Lens, p < f

n  The image is virtual n  The image is upright

Ray Diagram for Diverging Lens

n  The image is virtual n  The image is upright

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Problem 23.36, p 786

n  The nickel’s image in the figure has twice the diameter of the nickel when the lens is 2.84 cm from the nickel. Determine the focal length of the lens.

Problem 23.59, p 788 n  The figure shows a converging lens with radii R1 = 9 cm and

R2 = 11 cm, in front of a concave spherical mirror of radius 8 cm. (a) If the focal points F1 and F2 are 5 cm from the vertex of the thin lens, what is the index of refraction of the lens? (b) If the lens and the mirror are 20 cm apart and an object is placed 8 cm to the left of the lens, what is the position of the final image and its magnification as seen by the eye in the figure? (c) Is the final image real or inverted?

Answer to 23.36 Answer to 23.59

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Answer to 23.59 (cont’d)