Image Formation

1
Image Formation and Optical Instruments
2
Simple Lens
A simple lens is an optical device which
takes parallel light rays and focuses them to a
point. This point is called the focus or focal
point f
Snells Law, applied at each point on the
surface, determines where the light comes to a
focus.
3
Simple Lens
4
Image Formation in a Lens

• The formation of images by a lens can be
  determined
• using two alternative approaches
• Using ray tracing. In this case a small number of
  
• characteristic rays are used.
• b) Using the Thin Lens equation and the
  Magnification
• equation. These equations relate the object and
  image
• distances, to the focal distance and
  magnification,
• respectively.

5
Image Formation in a Lens Ray Tracing

• The three basic light rays used in ray tracing
• A ray which leaves the object parallel to the
  axis, is refracted to pass through the focal
  point (P).
• 2. A ray which passes through the lenss center
  is undeflected (M).
• 3. A ray passing through the focal point (as
  shown)is refracted to end up parallel to the
  axis (F).

6
Images Formed by a Convex Lens
7
Images Formed by a Concave Lens
8
The Thin Lens Equation
9
Sing Conventions
1. Converging or convex lens focal length is
positive image distance is positive when on
the other side of the lens (with respect to
object) height upright is positive, inverted
is negative 2. Diverging or concave lens focal
length is negative image distance is always
negative (on the same side of the lens as the
object) height upright is positive, inverted
is negative
10

• The image is twice as large as the object
• and is located 15 cm from the lens. Find
• The focal length
• The object distance

11

• An object of height 3 cm, is placed 12 cm in
  front of a diverging
• lens with a focal length of 7.9 cm.
• Use ray tracing to form the image
• Use the thin lens equations to find the image
  distance and size

12

• An object of height 3 cm, is placed 12 cm in
  front of a diverging
• lens with a focal length of 7.9 cm.
• Use ray tracing to form the image
• Use the thin lens equations to find the image
  distance and size

13

• An object of height 3 cm, is placed 12 cm in
  front of a diverging
• lens with a focal length of 7.9 cm.
• Use ray tracing to form the image
• Use the thin lens equations to find the image
  distance and size

14
The Lensmakers Formula
The lens formula correlates the focal distance,
the object distance, and the image distance
1/f 1/l 1/l The lensmakers formula
gives the focal distance f, as a function of R1
and R2, the radii of curvature of the two
surfaces of the lens.
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The Human Eye
The eye produces a real, inverted image in the
retina. The Ciliary muscles change the shape of
the lens, adjusting the focal length according
to the object distance. The amount of light that
enters the eye is controlled by the iris, that
expands or contracts to adjust the pupil size
16
The Camera
The camera forms a real, and inverted image, on a
photographic film, or a solid state sensor
The camera focuses by moving the lens back and
forth. The aperture of the camera can be adjusted
Small f-number ? large aperture
The amount of light that enters the camera is
controlled by the f-number (i.e 5.6) and the
shutter speed (i.e.1/250).
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The Angular Size of an Object
The image of the object subtends an angle ?
on the retina. ? ? ho / do The larger ?, the
larger the object appears to be. The closest
object distance at which the eye can focus is the
near point N. N ? 25 cm (young) N ? 40 cm (not
so young)
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The Magnifying Glass

• Object at near point ? ? ho / N
• If a lens with focal distance f
• (f lt N), is placed in front of the eye,
• and the object is placed at f,
• the image forms at infinite,
• with angular size ? ? ho / f.
• Since f lt N ? ? ? ?, and
• the object appears magnified.
• Angular magnification
• M ? / ? ? N / f

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The Compound Microscope
The objective has short focal distance. The
object is placed just beyond the focal point.
A real, inverted, enlarged, image is formed, at
or near the focus of the eyepiece. The
eyepiece works as a magnifier, producing a
further magnified image.
The distance between the lenses is larger than
the sum of focal lengths. The total magnification
is the product of each lens magnification. M ? -
(di / fobjective) (N / feyepiece)
20
The Telescope
Telescopes deal with objects that are infinitely
far away. The image formed by the objective is at
its focal point, (and at the focal point of the
eyepiece). The eyepiece works as a magnifier,
producing a further enlarged image. The
distance between lenses is about the sum of the
focal lengths. The angular magnification is M
? / ? fobjective / feyepiece