Transcript converging lens

Lenses
Physics 202
Professor Lee Carkner
Lecture 23
Refraction
Mirrors can be used to magnify an object or
to gather light
Lenses can be used for the same purposes
Lenses gather light and magnify objects
through refraction instead of reflection
Lenses have focal lengths and real and virtual
images, but their properties also depend on
the index of refraction
Unlike a mirror, you look through a lens
It has two sides we have to account for
Lenses
Light incident on a lens is refracted twice,
once when entering and once when leaving
We will consider only thin lenses, i.e.
thickness much smaller than i, p or f
Our thin lenses are composed of two
refracting surfaces placed back to back
If the two surfaces are the same, the lens is
symmetric
Lenses and Mirrors
Mirrors produce virtual images on the opposite
side from the object
Lenses produce virtual images on the same side as
the object
i is negative in both cases
Mirrors produce real images on the same side
as the object
Lenses produce real images on the opposite side as
the object
i is positive in both cases
If a mirror curves towards the object, f and r
are positive (real focus)
If a lens curves towards the object, f and r are
negative (virtual focus)
Real is positive, virtual is negative
Converging and Diverging
Converging Lens
A lens consisting of two convex lenses back to
back is called a 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
f is real and positive
Converging lenses produce images larger
than the object
Magnification is same as for mirrors
m = -i/p
Diverging Lens
A lens consisting of two concave lenses back
to back is called a 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
Th focal point is on the same side as the
incoming rays
Diverging lenses produce images smaller
than the object
Converging and Diverging
Lens Equations
A thin lens follows the same equation as a
mirror, namely:
1/f = 1/p + 1/i
We can also relate f to the index of refraction
of the lens n
1/f = (n-1) (1/r1 -1/r2)
Where r1 and r2 are the radii of curvature of
each side of the lens (r1 is the side nearest the
object)
If the lens curves towards the object, r is negative,
if the lens curves away from the object, r is
positive
For symmetric lenses r1 and r2 have opposite sign
Three Types of Images
Converging Lenses and Images
The type of image produced by a converging lens
depends on the distance of the object from the
focal point
Objects in front of the focal point (nearer to the
lens) produce virtual images on the same side as
the object
The image is not inverted
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
The image is inverted
Image is real so i is positive
Diverging Lenses and Images
No matter where the object is, a diverging
lens produces an upright, virtual image on
the same side as the object
For either lens the location of images is the
reverse of that for mirrors:
Virtual images form on the same side as the
object, real images form on the opposite side
Real images have positive i, virtual images have
negative i
Three Types of Images
1) Rays that are initially parallel to the central
axis will pass through the focal point after
refraction and vice versa
2) Rays that pass through the center of the lens
will not be refracted
Two Lenses
Many common optical instruments are
formed from more than one lens (microscope,
telescope)
To find the final image we find the image
produced by the first lens and use that as the
object for the second lens
For a two lens system the magnification is:
M = m 1m2
Dual
Lenses
Optical Instruments
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
Near Point
You can increase an objects angular size by
moving it closer to your eye
The largest clear (unlensed) image of an
object is obtained when it is at the near point
(about 25 cm for most people)
If you move the object any closer it will not be
in focus
A converging lens will increase the angular
diameter of an object
mq = q’/q
Magnifying Lens
You can use a magnifying lens to overcome
the limitation of your eye’s near point
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:
mq = 25 cm /f
This is the size of the object seen through the
lens compared to its size at the near point
Magnifying Glass
Compound Microscope
A simple compound microscope consists of an
objective and eyepiece
The objective creates a real image focused at the focal
point of the eyepiece
The eyepiece acts as a magnifying glass
The magnification of the objective is m = -i/p
i is very close to the distance between the lenses, s
p is very close to the focal length of the objective, fob
The total magnification is the product of the
magnification of each
M = (-s/fob)(25 cm/fey)
where s is the distance between the focal point of the
lenses (the tube length) and f is the focal length
Microscope
Refracting Telescope
In a telescope the two lenses are placed so
that the two inner focal points are in the same
place
The rays coming in from infinity are refracted by
the objective to create a real image at the common
focal point
The eyepiece then magnifies the real image
The total angular magnification of the
telescope depends on the ratio of the
eyepieces
mq = -fob/fey
Refracting Telescope
Telescopes
The magnification of the telescope can be altered by
changing eyepieces
Short focal length means more magnification
Magnification is not the most important property of
a telescope
Limited by blurring effects of atmosphere
The true purpose of the objective lens is to gather
more light than your eye can and focus it so that it
can be viewed
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
Most large telescopes are reflectors
Giant 40 inch
Refractor
at Yerkes
Observatory,
Williams Bay
Wisconsin
Newtonian Telescope