Transcript optical instruments

Cameras
• Major components
•
•
•
•
Lens (or combo)
Film (or CCD)
Aperture
Shutter speed
Cameras
• Lens
• Single focus lens
• Zoom Lens (vary
distance between the
lenses to change the
effective focal length
(see example)
Example: A compound camera lens
p1
q1
q2
p2
A camera lens is usually a combination of two or more single lenses.
Consider a camera lens consisting of a diverging lens with f1 = -120 mm and
a converging lens with f2 = 42 mm, spaced 60 mm apart. A 10 cm tall
object is 500 mm away from the first lens.
(a) What are the location, size, and orientation of the image?
p1 = 500 mm

1 1  
1
1


q1   -   

 f1 p1   - 120 mm 500mm 
q2 = 97 mm + 60 mm = 157 mm
1
1 

1
-1
 -97 mm
1

-1
  57 mm
q2   -   

 f2 p2   42mm 157 mm 
Example: A compound camera lens (continued)
p1
q1
p2
q2
qs ' (-97 mm)
 0.194
MM1 1 - 11  s
(500
mm)
p11
qs22 '
(57 mm)


 -0.363
MM

2 2
(157 mm)
ps22
M  M1M 2  (0.194)(-0.363)  -0.070
h '  hM  (10 cm)(-0.070)  -0.70 cm
(b) What is the focal length of the single lens that could produce an image
at the location if placed at the midpoint of the lens combination?
-1
-1


1
1
1 1 
f eq      

  75 mm
 sp qs ' 
 (530 mm) (87 mm) 
Exposure
• What do we need for a well exposed
picture?
Exposure
• What do we need for a well exposed
picture?
• Enough Energy on the film (i.e. light)
• A more sensitive film needs less light, a
less sensitive film needs more light.
Film Sensitivity (ISO #)
• more sensitive film (e.g. ISO 1000)
• Advantage: can take picture in low light
• Disadvantage: grainier picture (light
sensitive chemicals are larger in size)
What factors control how much
energy gets to the film?
Condition
• 1a. Opening of lens
(Aperture)
• 1b. Focal length of
lens
How do I control it?
• 2. Time of exposure
• 2. shutter speed
• 1. f-stop
Camera Lenses: f-stop
D
f
In camera notation, the “f-stop” means the ratio f/D, where f is
the focal length of the lens and D is the diameter of the aperture.
f
f - stop 
D
f small and D big means
small f-stop (e.g. f/4) a lot of light
f big (tele lens) and D small means
big f-stop (e.g. f/22) little light
Camera Lenses: f-stop and exposure times
D
f
In camera notation, the “f-stop” means the ratio f/D, where f is
the focal length of the lens and D is the diameter of the aperture.
Thus, f /5.6 means that f/D = 5.6. If f = 50 mm, then D = 8.93 mm.
The exposure time t is proportional to (intensity)-1 or to D-2.
Example: A camera needs a t1 = 1/100 s exposure time to make an
photograph at f/16. What exposure time is needed at f/4?
2
2
t 1  D2   f / 4   16 

 
     16
t 2  D1   f /16   4 
2
t 2  t1 /16  (1/100 s) /16  1/1600 s
Lens Aberrations
Because the index of refraction
depends on wavelength, a lens will
focus different wavelengths at
different focus positions.
Because the focal condition is based
on the small angle approximation,
spherical lenses focus large-angle rays
at different focus positions.
Cure: Compound lenses made of
Cure: Compound lenses including
glasses with different dispersions.
elements with non-spherical shapes.
Acromatic Lens
crown
glass
flint
glass
By combining a converging lens of crown glass (n = 1.522) with a
color-compensating diverging lens of flint glass (n = 1.805),
chromatic aberration can be eliminated.
Camera and Eye
• Camera: change distance between lens
and film (focal length f=const)
• Eye: distance between lens and retina is
constant!!! What can be changed?
Focal length f is changed through
accomodation.
The eye is most sensitive to light of about 550 nm. That is also
the wavelength that the Sun emits most strongly at.
Far and near point
• Far Point (normal
eye, relaxed): infinity
• Near Point: Minimum
distance that can be
focused (max.
accommodation):
25cm
Nearsightedness
•
•
•
When fully relaxed, a nearsightedness eye will not
be able to focus a distant object on the retina. The
image will be in front of the retina. Part a.
The far point FP of a nearsighted person is less
than infinity. Part b.
The correction for nearsightedness involves a
diverging lens. Part c.
Nearsightedness - Example
A nearsighted woman has a near point of 12 cm and a far point of 17
cm (without correction), i.e. she can only focus on objects that are
located between these two distances.
a.
Find what focal length contact lens is needed for her to see distant
objects clearly.
b. Find her new near point (with the contacts on).
Example: Correcting Nearsightedness
A nearsighted woman can see objects clearly only when they are
from 12 cm to 17 cm from her naked eye. Find what focal length
contact lens is needed for her to see distant objects clearly. Also
find her new near point (with the contacts on).
We want the contact lens to put the image of a distant object
(at infinity) at her far point (17 cm). So q = -17 cm and
1
1
1
 
f  - 17 cm
f = -17 cm
The minus sign indicates it
is a diverging lens.
To find her new near point, realize that the contacts place the
image of the nearest object that can be seen clearly at her naked
eye near point (12 cm from her eye). So q = -12 cm and
1
p

1
f
-
1
q

1
1
- 17cm - 12cm
p = 40.8 cm
When wearing contacts, she can see
clearly from 40.8 cm out to infinity.
Microscope
The front objective lens
produces a real magnified
image I1, which is then
further magnified by the
eyepiece.
The Microscope
• A specimen to be observed is placed on the stage
of a microscope, directly beneath the objective, a
converging lens with a relatively short focal length.
• The objective creates a magnified real image that is
further enlarged by the eyepiece.
• The lateral magnification of the objective is
• Together, the objective and eyepiece produce a total
angular magnification
Microscope
• Objective lens: converging with small f
• Eyepiece: simple magnifier
• Objective lens produces real, inverted and
enlarged image
• Eyepiece enlarges it further and produces
a virtual image
Microscope
•
•
you can’t see the virtual image
in the diagram. It is located far
away, so that we can view it
with a relaxed eye (do2=inf)
Objectiv
The Telescope
• A simple telescope contains a large-diameter
objective lens which collects parallel rays from a
distant object and
forms a real, inverted image
at distance s' = fobj.
• The focal length of a telescope objective is very
nearly the length of the telescope tube.
• The eyepiece functions as a simple magnifier.
• The viewer observes an inverted image.
• The angular magnification of a telescope is
Refracting Telescopes
Galilean telescope: Eyepiece is a short-focus diverging lens placed
before the focus of the long focal-length objective lens. The
resulting magnified image is upright (because the rays don’t cross).
Keplerean telescope: Eyepiece is a short-focus converging lens
placed after the focus of the long focal-length objective lens. The
resulting magnified image is inverted (because the rays cross).
Reflecting Telescopes
Newtonian telescope
Cassegrain telescope