1. Optics –Physics 4510 Photography M. Goldman
The Camera and Photography
Parts of the camera
The shutter, speeds and motion blur
The diaphragm, aperture control, stops and f-numbers
Exposure
Optics of cameras
Cameras with lenses versus pinhole cameras
Focusing, depth of focus and depth of field
Telephotos and wide-angle lenses

2. One of many rays of light shining on Alex
Object photographed with a pinhole camera yields real upside-down image without any lens
One of many rays of light shining on Alex
Pinhole Camera
Rays from the real Alex go through the hole
and make the image
blocked rays
Image of Alex
Alex

3. previously blocked rays
If a lens is used instead of a pinhole the image is brighter because many of the previously blocked rays are bent so that they arrive at the correct place on the screen image
Camera with lens
Pinhole Camera
blocked rays
previously blocked rays
Image of light bulb
Light bulb
Not just ONE ray from the filament but MANY now arrive at the corresponding image point so the image is BRIGHTER
Show with bellows camera by opening up lens

4. A telephoto effect (enlarged image) for a pinhole camera only requires increasing the distance from pinhole to camera back
As the distance between the pinhole and the back of the pinhole camera is increased the image increases in size
This is a telephoto effect
The image ALWAYS STAYS IN FOCUS (sharp) because for a pinhole camera there is only one ray connecting each object point to each image point

5. A telephoto effect (enlarged image) for a camera with a LENS requires increasing the distance from lens to camera back AND increasing the focal length of the lens to keep the image in focus
As the distance between the lens and the back of the camera is increased the image remains in the same place
It is no longer in focus at the back of the camera
It is in focus at the same place as before
x0 and f are the same so xi must be at the same place
In addition to increasing the distance between the lens and the back of the camera the focal length of the lens must be increased by the right amount!
The new image is larger and in focus f f
Note that can always make the image larger by bringing the camera lens a lot closer to the ojbect. This does not require a change in focal length. Example of pinhole camera at three different locations. Show on video camera with zoom lens and manual focus
fnew

6. A telephoto effect is achieved in cameras in a variety of ways
Zoom lens focal length can be adjusted and changed
Advanced photographers use interchangeable lenses with different focal lengths for different effects
Distance, xi, from lens to back of camera must be adjusted for each different focal length, f.
xi = special distance at which rays from an object point all come together (intersect) at image point
This is called focusing
At other distances, x, image at camera back is out of focus

7. How does a camera with a lens differ from a pinhole camera?
Pinhole camera: "one" ray goes from each object pt. to corresponding pt. at camera-back (where image falls on film or CCD).
Image is relatively dim because only one ray from each object point reaches it
Image from pinhole camera is ALWAYS IN FOCUS (no matter what distance is from lens to camera back)
When increase distance from lens to back of camera image is magnified and stays in focus
Camera with lens allows many rays from each object pt to be sent to corresponding image pt. at back of camera (where it registers image on CCD).
Bright image because many rays from each object pt reach each image pt.
Lens focal length determines where transmitted rays cross to form image pt. of each object pt.
Telephoto or "zoom" effect
Increase distance from lens to film to make image larger.
This puts image out-of-focus.
To keep it in focus must also change focal length of lens

8. Parts of camera
Back of camera where film or CCD (for digital camera) is
Lens - can be moved closer to camera back or further away.
This is called focusing
Lens can have fixed focal length or variable focal length (zoom)
Diaphragm - decreases usable diameter of lens in steps
Shutter - The shutter lets light from object reach lens and film (or CCD) for a limited, controlable time
Shutter "speed"
Shutter and diaphragm together control how much light reaches camera back
They control the exposure
On automatic cameras adjustment of the exposure (diaphragm/shutter) is done automatically.
Show viewgraph 4.1
Show diaphragm

9. Parts of camera illustrated
Single-lens reflex
Point and shoot digital

10. What is depth of focus of camera lens?
Range of lens-to-cameraback distances for which one image is tolerably sharp (reasonably in focus)
Infinite for pinhole camera
image is always in focus
≈ one ray connects each object pt to image pt
For lens-camera depth of focus depends on
lens diameter,
focal length and
object distance
Circle of confusion
locus of rays that focus to pt elsewhere
If diameter of circle of confusion is small enough blur is tolerable
Lens with smaller diameter has larger depth of focus
More like a pinhole (image is dimmer)
circles of confusion
image blurry here but tolerable
depth of focus f f
missing ray
smaller circle of confusion
Show this with large lens and one illuminated arrow
Show with smoke machine that lenses aren't perfect anyway

11. What is depth of field of a lens?
related to depth of focus
maximum separation distance (along axis) between two objects such that both objects are tolerably sharp (in reasonably good focus)
Deep focus: term for large depth of field in movie-making
Pinhole camera depth of field is ∞
all objects in focus at all lens-to- camera-back distances.
Smaller lens opening (aperture) ⇒
larger depth of field but
dimmer image
Wide angle lenses generally have more depth of field than telephotos
Depth of field
diameter of
circle of confusion (maximum tolerable blur)
Show with large lens and two illuminated arrows
Show how use of a stop improves the resolution and the depth of field

12. Circles of confusion

13. A camera is focused by changing the distance between the lens and the film or CCD at the back of the camera
xi in lens eqn is distance between lens and back of the camera (where image is recorded)
1/f = 1/xo + 1/xi
Suppose you take a picture of your friend using a camera with a lens of focal length f = 1 cm
The friend is a distance xo = 100cm from the camera lens
For what value of xi is the image at the back of the camera in focus?
The value obtained by solving the lens eqn for xi
100 cm
Roughly the same as the focal length, f
Given: f = 1 cm, xo = 100 cm
Find: image distance, xi
1/f = 1/xo + 1/xi
1/1 = 1/ /xi
= 1/xi
0.99 = 1/xi
xi = 1/0.99 = 1.01 cm
Both (a) and (c) are both correct
When take picture of object a distance xo away from camera which is much larger than the focal length, f, the image distance, xi, will always be a number very close to f
This is because rays from distant object are almost parallel and therefore go through the focal point!!
Can also see from lens equation

14. What are apertures, f-numbers and stops?
Diameter of lens aperture can be reduced by using diaphragm.
Largest aperture is full diameter of lens
Smaller apertures are called stops
Aperture is measured by f-number: focal length of lens divided by diameter of aperture:
f-number (or f-stop) = f/d
Large f-number means small lens diameter
What is f-number (f-stop) of same lens when diaphragm reduces dia-meter of lens from 10 mm to 5 mm?
40 mm focal length lens
at full aperture of diameter
d = 10 mm
40 mm focal length lens
with aperture of diameter d = 5 mm 10 5 10
f-number =  f
= 4 ( = f/4)
a) f/2, b) f/4, c) f/6, d) f/8, e) f/10
Show small diaphragm in class

15. Camera exposure is related to Poynting flux carried by light wave.
Wave energy density and flux of wave energy density ∝ E2
Flux of energy density =
Poynting flux [velocity×energy-density – (m/s)×J/m3]
Intensity [power/m2 - watts/m]
When brighter (more intense) light enters your eye
Electric force field of light is stronger (more photons)
More absorption in your retina (back of eye)
electric force fields add here
rays converge here

16. as smaller aperture lens
Lens with larger aperture lets more light energy reach image pts. at back of camera (where CCD records image)
Larger aperture lens brings more rays from each object pt. to corresponding image pt.
Pinhole only lets "one" ray from real nose converge at image nose.
Image is dim (not intense)
Small aperture lens lets a few more rays from nose converge to image nose.
Brighter image
Large aperture lens allows more rays from nose to con-verge to image nose.
Image even brighter
Why do we squint in bright light?
Pinhole
Small aperture lens
Large aperture lens
with same focal length
as smaller aperture lens

17. Light is more intense when there is more energy per unit area.
Intensity of light (Poynting flux)
= energy per second per unit area
Power = energy per second (watts)
Intensity = power divided by area
Power from 60 watt light bulb same as move away but intensity decreases
Alex sees intensity (power reaching his eye = intensity times his eye area)
Intensity ∝ 1/r2
r = distance from center of light bulb to your eye
Intensity falls off as square of the distance
Star seems dim!
Camera flash sometimes can't supply enough light? r
Light
bulb
Draw imaginary sphere whose radius, r =
distance from your eye to center of light bulb
Intensity of light is same everywhere on sphere = power divided by area of sphere
Area of sphere ∝ r2 so intensity ∝ r-2

18. Light energy reaching film each second is proportional to the AREA of lens
Camera
Light energy/s  lens area, A
A  d2
d  √A
If A is doubled by what factor does d increase? √2 2 4
Lens
diameter of lens = d d
Area of lens = A = π(d/2)2

19. More light energy reaches ccd when lens f-stop is lower number (lower number means larger area)
f-stop = (focal length)/d
f-stop at right has diameter d = 5 so f-stop is 40/5 = 8
Double diameter, d from 5 to 10 mm
New f-stop is 40/2d = 4
New area of aperture, A, increases by factor 4
Lets in 4 times amount of light energy/s (since energy  Area)
To double energy reaching CCD:
Multiply old diameter, d, by √2
New area is doubled because √22 = 2
New f-stop (√2d) decreased by factor of 1/√2 from f/8 to f/5.6
f = 40 mm lens
with aperture d = 5 mm 5
5·√2
40 mm lens
at full aperture 2d = 10 mm 10
new diameter = √2·d mm
= 7.1 mm
40/(√2·d) = f/5.6
40/d = f/8
40/(2d) = f/4
Area = π ·(d/2)2 = mm2
Area = π ·(√2·d/2)2 = mm2 (2x energy as at f/8)
Area = π·(2d/2)2 = 25 mm2 (4x energy as at f/8)

20. Sequence of f-stops which each let in twice the light energy per sec
Smaller f-stops mean larger diameters, less depth of field, larger aperture areas and more light energy gets to CCD
f-stop or f-number = (focal length)/(lens diameter)
Each f-stop down list
has diameter, d, larger by factor √2 than the previous stop
has aperture area (d2) larger by factor 2
Lets in twice the light energy (energy  area)
Smaller f-stops

21. A light wave continues to deliver energy as long as the wave keeps moving into an eye or a lens
You get more of a sunburn if the suns rays hit your skin longer
Each second more light energy hits your skin
Less light energy goes into your your eye if you open and close it again quickly
More light arrives at CCD at back of a camera when shutter is left open longer
Image gets brighter if shutter is left open longer

22. Sequence of shutter speeds in which each faster speed lets in half the light energy
1/15 sec
1/30 sec
1/60 sec
1/125 sec
1/250 sec
1/500 sec
1/1000 sec
1/2000 sec
Faster speeds, better able to stop (freeze) fast motion but give darker image

23. What is meant by exposure of a picture?
Exposure at CCD is proportional to total light energy falling on CCD during time shutter is left open
Intensity of light on CCD = energy delivered per second divided by AREA of CCD
Exposure ∝ light intensity × time interval shutter is open
Exposure depends on both f-stop (controls intensity) and
shutter speed (time shutter is left open)

24. Large depth of field because of small aperture,
Equivalent combinations of f/stops and shutter speeds (which deliver the same energy to the film or CCD). All give same exposure!
f/22
f/16
f/11
f/8
f/5.6
f/4
f/2.8
f/2
f/1.4
1/15 sec
1/30 sec
1/60 sec
1/125 sec
1/250 sec
1/500 sec
1/1000 sec
1/2000 sec
1/4000 sec
Large depth of field because of small aperture,
but slow shutter speed near top of list may give motion blur
Fast shutter speed but small depth of field near bottom of list due to large apertures.
but image may be out of focus due to small depth of field
Twice the energy gets in each second
Half the time for energy to get in

25. Which exposure lets in more light?
Different exposures correspond to different alignments of sequence of f-stops and sequence of shutter speeds
1/15 sec
1/30 sec
1/60 sec
1/125 sec
1/250 sec
1/500 sec
1/1000 sec
1/2000 sec
1/4000 sec
f/22
f/16
f/11
f/8
f/5.6
f/4
f/2.8
f/2
f/1.4
f/22
f/16
f/11
f/8
f/5.6
f/4
f/2.8
f/2
f/1.4
1/15 sec
1/30 sec
1/60 sec
1/125 sec
1/250 sec
1/500 sec
1/1000 sec
1/2000 sec
1/4000 sec
Which exposure lets in more light?

26. More detailed examples of equivalent exposures
Exposure time
1/250 sec
1/125 sec
1/60 sec
1/30 sec
f-number
f/5.6
f/8
f/11
f/16
Diameter of 28mm lens
5 mm
3.5mm
2.5mm
1.75mm
Area of aperture of 28 mm lens
20 mm2
10 mm2
5 mm2
2.5 mm2
Light intensity reaching film (arb units)
500
250
120 60
Exposure (arb. units) 2

27. How we can understand the concept of intensity in terms of the images from pinhole cameras.
Intensity of light is energy/second per unit area (e.g., watts per m2)
Light is more intense when there is more energy delivered to each unit area each second
How does the intensity change when the image is larger? Is the intensity of light on the film of the telephoto camera
higher, b) lower, c) the same
The same light energy is spread over a larger area so the intensity goes down
To compensate for this lower intensity cameras use a lens to let in more light than a pinhole can.

28. Qualitative argument why f-number is defined as f/d
Qualitative argument why f-number is defined as f/d. (focal length divided by lens aperture diameter)
Consider two lenses with different focal length but same f-number, say, f/2
f/2 lens with longer focal length, f, must have larger diameter, d, by definition f-number = f/d
Larger d brings more rays to each image point
If d were not larger, image would be less intense (dimmer, as in pinhole camera)
Definition f-number = f/d
guarantees that every f/2 lens gives same exposure for the same shutter speed
regardless of whether focal length, f, is small (wide-angle lens) or large (telephoto lens).
Quantitative proof on next slide
f = 40 mm
20 mm
f/2 lens with focal length 40 mm means 2= 40/d, so lens has diameter d = 20 mm
f/2 lens with focal length 60 mm means 2= 60/d, so lens has diameter d = 30 mm
30 mm
fnew = 60 mm

29. Quantitative argument why two lenses with same f-numbers give image of Alex with same intensity
If fnew= 60 mm lens did not have larger diameter than f = 40 mm lens, the intensity, Iimage of its image would
be lower by 1/xi2, where xi is distance from center of lens to Alex's image
Object is usually far from lens so rays enter lens almost parallel and xi ≈ f
For same d, Iimage decreases as 1/fnew2
Doubling f2 decreases Iimage by factor 2
For same f, Iimage increases as d2
Doubling d2 increases Iimage by factor 2
Different focal length lenses only have same Iimage if d2/f2 is same for both.
Ratio d2/f2 = 1/(f-number)2
If both lenses have same f-number there is no change in image intensity
20 mm
f = 40 mm
f/2 lens with f = 40 mm must have d = 20 mm
f/2 lens with f = 60 mm must have d = 30 mm
30 mm
fnew = 60 mm

30. Common focal lengths, f, of f/2
Common focal lengths, f, of f/2.8 lenses and required diameters for each
Lens focal length, f
35mm
50mm
80mm
105mm
135mm
Max f/stop
f/2.8
d = lens diameter = f/(f/stop)
12.5mm
17.9mm
28.6mm
37.5mm
48.2mm

31. Wide angle and telephoto effects in the pinhole camera only depend on distance from pinhole to film
As distance between pinhole and cam-era back increases, image gets larger
First camera gives wide-angle effect
camera back is covered by image that includes more than Alex
Longer camera gives telephoto effect
Alex's image covers entire camera back
Angle between crossed yellow lines smaller in longer camera
Image alwayss in focus (sharp)
Wide angle and telephoto lenses have some similarities to pinhole camera
Telephoto lenses are long and wide angle lenses are short
There are also differences
Lens lets in more light ⇒ brighter image
f must be different for different image sizes to maintain focus
smaller angle

32. Digital and 35 mm camera lenses compared (lens may be a zoom lens)
Focal Length of digital camera lens
Equivalent focal length of 35mm film camera lens
Image appearance
Typical Uses
5.4 mm
35 mm
Object looks smaller and farther away.
Wide-angle shots, landscapes, large buildings, groups of people
7.7 mm
50 mm
Object looks about same as what eye sees.
"Normal" shots of people and objects
16.2 mm
105 mm
Object is magnified and appears closer.
Telephoto shots, close-ups

33. Meaning of ISO on digital cameras
ISO measures sensitivity of CCD at image plane
Formerly a measure of film sensitivity (film "speed")
High ISO number means
high sensitivity of CCD
take pictures with less light
or at smaller f/numbers with greater depth of field
However pictures taken at high ISO have less resolution
They are pixelated or grainy

34. Comparison of images