physics 1202: lecture 23 today’s agenda announcements: –lectures posted on: rcote/ rcote/ –hw...
DESCRIPTION
Mirror – Lens Definitions Some important terminology we introduced last class, –o = distance from object to mirror (or lens) – i = distance from mirror to image o positive, i positive if on same side of mirror as o. –R = radius of curvature of spherical mirror –f = focal length, = R/2 for spherical mirrors. –Concave, Convex, and Spherical mirrors. –M = magnification, (size of image) / (size of object) negative means inverted image R object h image o iTRANSCRIPT
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Physics 1202: Lecture 23Today’s Agenda
• Announcements:– Lectures posted on:
www.phys.uconn.edu/~rcote/– HW assignments, etc.
• Homework #7:Homework #7:– Due next FridayDue next Friday
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oi
fh’
h
Rh
h’o-R
R-i
oi
&
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Mirror – Lens Definitions• Some important terminology we introduced last class,
– o = distance from object to mirror (or lens)– i = distance from mirror to image
o positive, i positive if on same side of mirror as o.– R = radius of curvature of spherical mirror– f = focal length, = R/2 for spherical mirrors. – Concave, Convex, and Spherical mirrors.– M = magnification, (size of image) / (size of object)
negative means inverted image
R
object
h
image
o
i
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Summary• We have derived, in the paraxial (and thin lens) approximation,
the same equations for mirrors and lenses:
when the following sign conventions are used:
Variable
f > 0f < 0
o > 0o < 0
i > 0i < 0
Mirror
concaveconvex
real (front)virtual (back)
real (front) virtual (back)
Lens
convergingdiverging
real (front)virtual (back)
real (back) virtual (front)
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This could be used as a projector. Small slide on big screen
This is a magnifying glass
This could be used in a camera. Big object on small film
UprightEnlargedVirtual
InvertedEnlargedReal
InvertedReducedReal
3 Cases for Converging Lenses
Image Object
Inside F
ObjectImage
Past 2F
ImageObject
BetweenF & 2F
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1) Rays parallel to principal axis pass through focal point.2) Rays through center of lens are not refracted.3) Rays toward F emerge parallel to principal axis.
F
F
Object
P.A.
Image is virtual, upright and reduced.
Image
Diverging Lens Principal Rays
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Lecture 23, ACT 1• A lens is used to image an object on a
screen. The right half of the lens is covered. – What is the nature of the image on the
screen?(a) left half of image disappears(b) right half of image disappears(c) entire image reduced in intensity
object
lens
screen
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Multiple Lenses • We determine the effect of a system of lenses by considering the
image of one lens to be the object for the next lens.
For the first lens: o1 = +1.5, f1 = +1
For the second lens: o2 = +1, f2 = -4
f = +1 f = -4
-1 +3+10 +2 +6+5+4
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Multiple Lenses • Objects of the second lens can be virtual. Let’s move the second lens
closer to the first lens (in fact, to its focus):
For the first lens: o1 = +1.5, f1 = +1
For the second lens: o2 = -2, f2 = -4
Note the negative object distance for the 2nd lens.
f = +1 f = -4
-1 +3+10 +2 +6+5+4
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Multiple Lenses • If the two lenses are thin, they can be touching – i.e.
in the same position. We can treat as one lens.ftotal = ??
?
Adding,
For the first lens: o=o1, i1 and f1
For the second lens: o2 = -i1, i2=i, f2
As long as,
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The Lens Equation– Convergent Lens:
if
h’o
h
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The Lensmaker’s Formula• So far, we have treated lenses in terms of their focal lengths. • How do you make a lens with focal length f ?
• Start with Snell’s Law. Consider a plano-convex lens:
Snell’s Law at the curved surface:
The bend-angle is just given by:
The bend-angle also defines the focal length f:
The angle can be written in terms of R, the radius of curvature of the lens :
Putting these last equations together,
RNair air
h light ray
Assuming small angles,
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More generally…Lensmaker’s Formula
Two curved surfaces…
Two arbitrary indices of refraction
R > 0 if convex when light hits it
R < 0 if concave when light hits it
The complete generalized case…
Note: for one surface Planar,
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Compound Microscope
o1
h
O
I2h2
feye
h1
I1
i1
Objective(fob< 1cm)
fob
L
Eyepiece(feye~5cm)
Magnification:
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Refracting Telescope
Starfeye
I2h2
fob
Objective(fob~ 250cm)
Eyepiece(feye~5cm)
i1I1
h1
AngularMagnification:
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~fe
I1
eyepiece
I2
~fo
objectiveLThe
EYE
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Retina
To brain
The Eye• What does the eye consist of?
– Sphere (balloon) of water.- An aperture that controls how much light gets through – the Iris/pupil- Bulge at the front – the cornea
- A variable focus lens behind the retina – the lens- A screen that is hooked up to your brain – the retina
Cornea
Iris Lens
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