Transcript (F). - UCF Physics

Image Formation
and Optical Instruments
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
f
•
Snell’s Law, applied at each point on the surface,
determines where the light comes to a focus.
Simple Lens
Convex lens compared to pair of prisms
Concave lens compared to pair of prisms
Image Formation in a Lens
The formation of images by a lens can be determined
using two alternative approaches:
a) 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.
Image Formation in a Lens – Ray Tracing
The three basic light rays used in ray tracing:
1. 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 lens’s center is
undeflected (M).
3. A ray passing through the focal point (as shown)
is refracted to end up parallel to the axis (F).
Images Formed by a Convex Lens
f
2f
f
f
Object between 2f and f
Image is inverted, real
enlarged.
f
2f
2f
2f
Object between f and lens
Image is upright, virtual,
and enlarged.
Images Formed by a Concave Lens
f
2f
f
Object beyond 2f.
Image is upright,
virtual, reduced.
f
f
2f
2f
2f
Object between
f and lens.
Image is upright,
virtual, reduced.
The Thin Lens Equation
h0
hi

f di  f
ho hi

do
di
Thin Lens Equation
1 1 1
 
do di f
Magnification
di hi
m 
d o ho
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
The image is twice as large as the object
and is located 15 cm from the lens. Find:
a) The focal length
b) The object distance
An object of height 3 cm, is placed 12 cm in front of a diverging
lens with a focal length of – 7.9 cm.
a) Use ray tracing to form the image
b) Use the thin lens equations to find the image distance and size
An object of height 3 cm, is placed 12 cm in front of a diverging
lens with a focal length of – 7.9 cm.
a) Use ray tracing to form the image
b) Use the thin lens equations to find the image distance and size
An object of height 3 cm, is placed 12 cm in front of a diverging
lens with a focal length of – 7.9 cm.
a) Use ray tracing to form the image
b) Use the thin lens equations to find the image distance and size
1 1 1
1
1 1

 
   di  4.8cm
f d o di
7.9 12 d i
4.8  3

di
hi
   hi  
 1.2cm
do
ho
12 
The Lensmaker’s Formula
The lens formula correlates
the focal distance, the object distance, and the image distance
[1/f =1/l + 1/l’]
The lensmaker’s formula gives
the focal distance f, as a function of R1 and R2,
the radii of curvature of the two surfaces of the lens.
1 1 
1
  n  1   
f
 R1 R2 
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
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:
focal length
f
f - number 

aperture diameter D
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).
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)
The Magnifying Glass
Object at near point:   ho / N
If a lens with focal distance f
(f < 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 < N  ’  , and
the object appears magnified.
Angular magnification:
M = ’ /   N / f
Tan   
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)
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