HW3 . Grading scale for homeworks - will be adjusted to \%. . HW4 . HW #5 is assigned today – see the course web page; Monday Morning - Exam grades available in CULearn. . The Camera and Photography Using what we have learned about lenses and ray-tracing to understand:
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Using what we have learned about lenses and ray-tracing to understand:
Cameras with lenses versus pinhole cameras
Focusing, depth of focus and depth of field
Telephotos and wide-angle lenses
"New" subjects in photography
Parts of the camera
The shutter, speeds and motion blur
The diaphragm, aperture control, stops and f-numbers
ExposurePhysics 1230: LightandColorChapter 4
One of many rays of light shining on Alex
Rays from the real Alex go through the hole
and make the image
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
Image of light bulb
Not just ONE ray from the filament but MANY now arrive at the corresponding image point so the image is BRIGHTER
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 pointA telephoto effect (enlarged image) for a pinhole camera only requires increasing the distance from pinhole to camera back
It is no longer in focus at the back of the camera
It is in focus at the same place as before
x0and 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
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
Advanced photographers use interchangeable lenses with different focal lengths for different effectsA telephoto effect is achieved in cameras in a variety of ways
Lens - it can always be moved closer to the camera back or further from the back. This is called focusing
The lens can have a fixed focal length or can have a variable focal length (zoom)
Diaphragm - this decreases the usable diameter of the lens in steps
Shutter - The shutter lets light from an object reach the lens and the film (or CCD) for a limited, controlable time
The shutter and diaphragm together control how much light reaches the camera back
They control the exposure
On automatic cameras adjustment of the exposure (diaphragm/shutter) is done automatically.Parts of a camera
This range is infinite for a pinhole camera because the image is always in focus (one ray connects each object pt to each image pt)
For a lens camera the depth of focus depends on the diameter of the lens its focal length and the object distance
The circle of confusioncontains the rays that focus to a point elsewhere
If the diameter of the circle of confusion is small enough the blur is tolerable when the camera back is there
A lens with smaller diameter has a larger depth of focus because it is more like a pinhole (image is dimmer)
imageblurry herebut tolerable
depth of focus
smallercircle ofconfusionWhat is the depth of focus of a lens in a camera?
It is the maximumdistance along the axis by which two objects can be separated and still be reasonably in focus
Deep focus is the term for large depth of field in movie-making
The depth of field of a pinhole camera is infinite because all objects are in focus at all lens-camera back locations
A smaller lens opening (aperture) gives a larger depth of field but a dimmer image
Wide angle lenses generally have more depth of field than telephotos
circle of confusion(maximum tolerable blur)What is the depth of field of a lens?
The largest aperture is the full diameter of the lens
Smaller apertures are called stops
The aperture is measured by the f-number = focallength of the lens divided by the diameter of the aperture:
f-number (or f-stop) = f/d
Hence, a large f-number means a small lens diameter
What is the f-number (f-stop) of the same lens when the diaphragm reduces the diameter of the lens from 10 mm to 5 mm?
40 mm focallength lens
at full apertureof diameter
d = 10 mm
40 mm focallength lens
with apertureof diameterd = 5 mmWhat are apertures, f-numbers and stops?
= 4 ( = f/4)
a) f/2, b) f/4, c) f/6, d) f/8, e) f/10
that the same lens is used for viewing and taking pictures. A mirror in the body directs
the light from the lens up into a prism for viewing, then flips up out of the way just
before an exposure is made. These are extremely versatile instruments in the right hands
and can take beautiful pictures if used with care.
A d2 means A = const·d2
If d is doubled A increases by a factor of 4 no matter what the constant is!!
A = 0.785 d2
If d = 2.5, then A = 0.785·2.5·2.5 = 4.91
But if d is doubled from 2.5 to 5, then A = 0.785·5·5= 19.64 which is 4 times 4.91
It is even easier to use proportionality since the constant doesn't matter:
Double d by multiplying by 2
Note (2d)2 = 4d2 so the new area is 4 times the old area.Mini-lesson on proportionality
If the diameter is doubled by how much does the volume change?
a factor 2
a factor 4
a factor 6
a factor 8
(2d)3 = 23·d3 = 8·d3, so the answer is a factor of 2
The diameter of a circle is proportional to the square root of its area
If the area is made 4 times larger, by what factor is the diameter increased?
b) √2, c) 4
Ans: √(4A) = √4·√A = 2·√APractice questions
Consider Alex's image
A pinhole only lets one ray from his nose converge at the image nose.
Image is dim (not intense)
A small aperture lens makes more rays from his nose converge to the image nose.
Image is brighter (more intense)
A large aperture lens allows still more rays from his nose to converge to the image nose.
Image is still brighter (too intense)
Why do we squint in bright light?A lens with a largeraperture lets more light energy reach each point on the image at the back of a camera (where film or a CCD lies)
Small aperture lens
Large aperture lens
with samefocal length
as smaller aperture lens
Area, A, of lens is proportional to lens diameter, d, squared
Therefore, lens diameter, d, is proportional to square root of lens area
Double the area and d increases by what factor?
diameter of lens = dLight energy reaching film each second is proportional totheAREA of lens
Area of lens = A = π(d/2)2
The f-stop at right has diameter d = 5 and f-stop 40/5 = 8
Suppose we double thediameter, d
The new f-stop is 40/2d = 4
The new area of the aperture is proportional to the square of the new diameter: A d)2 = 4d2, an increase by a factor of 4
This lets in 4 times the amount of light energy (since energy Area)
How can we just double the energy reaching the film?
Multiply diameter, d, by number √2
The area (√2d)2 = √22d2 is doubled because √22 = 2
The f-stop (√2d) is decreased by a factor of 1/√2 from f/8 to f/5.6
40 mm focallength lens
with apertureof diameterd = 5 mm
40 mm lens
at full apertureof diameter
2d = 10 mmMore light energy reaches the film when the f-stop of the lens is decreased
new diameter= √2·d mm
= 7.1 mm
40/d = f/8
Area = π ·(√2·d/2)2= 12.5 mm2(twice the light energyas at f/8)
Area= π ·(d/2)2= 6.25 mm2
Area= π·(2d/2)2= 25 mm2(4 x the light energy as at f/8)
Smaller f-stops mean larger diameters, less depth of field, larger aperture areas and more light energy gets to film
f-stop or f-number defined as= (focal length)/(diameter of lens)
Each f-stop down the list
has a diameter, d, larger by factor √2 than the previous stop
has an aperture area (d2) larger by factor 2
Lets in twice the light energy (energy area)Sequence of f-stops which each let in twice the light energy per sec
Depth of field video
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 the CCD at the back of a camera when the shutter is left open longer
Image gets brighter if shutter is left open longerA light wave continues to deliver energy as long as the wave keeps moving into an eye or a lens
1/2000 secSequence of shutter speeds in which each faster speed lets in half the light energy
Faster speeds, better able tostop (freeze) fast motionbut give darker image
Sometimes the exposure is defined in terms of the intensityof light at the film
YouTube Video on shutter and aperature
The intensity of light on the film is defined as the energy delivered per second divided by the area of the film
The exposure is proportional to the lightintensity × the time interval that the shutter is left open
Hence the exposure depends on both the f-stop (which controls the intensity) and the shutter speed which is the time the shutter is left openWhat is meant by exposure of a picture?
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 inEquivalent combinations of f/stops and shutter speeds (which deliver the same energy to the film or CCD). All give sameexposure!
Power = energy per second (watts)
How many watts is that light bulb in your room?
Intensity = powerdivided byarea
Power comning out from light bulb is same as we move away (say, 60 watts)but intensity decreases
Alex sees intensity (power reaching his eye is intensity times his eye area)
Intensity is proportional to 1/r2
r is the distance from the center of the light bulb to your eye
Intensity therefore falls off as the square of the distance
Think of how dim a star seems!!
Why can't your camera flash sometimes supply enough light?
rLight is more intense when there is more energy per unit area.
Draw an imaginary sphere whose radius, r is thedistance from your eye to the center of the light bulb
The area of the sphere is proportional to r2 so the intensityis proportional to 1/r2
Light is more intense when there is more energy per unit area
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 we use a lens to let in more light than a pinhole can.How we can understand the concept of intensity in terms of the images from pinhole cameras.
Consider a lens with a different focal length but the samef-number:
It must have a larger diameter for a larger focal lengths (by definition)
The larger diameter lens brings more rays to each image point
so that the same light intensity arrives at the film (for same source)
If the lens were not larger the image would be less intense (dimmer), as in the pinhole camera
So the definition guarantees that every f/2 lens gives the same exposure for the same shutter speed, regardless of whether it's focal length is small or large (wide-angle or telephoto).
f = 40 mm
fnew = 60 mmWhy is the f-number defined as the focal length divided by the lens aperture diameter?
f/2 lens with focal length 40 mm means2= 40/d, so lens has diameter d = 20 mm
f/2 lens with focal length 60 mm means2= 60/d, so lens has diameter d = 30 mm
smaller by 1/xi2, where xi is the distance to Alex's image
But if Alex is far enough in front of the lens (a few feet) we found that xi is approximately the same as the focal length, f
Hence, the image intensity would decrease as 1/f2
To compensate, the larger lens diameter (d) lets in more intensity by the factor d2 (area)
The ratio d2/f2 = 1/(f-number)2 so that if both lenses have the same f-number there is no change in intensityWe can prove that two lenses with the same f-number give an image of Alex with the same light intensity
f = 40 mm
f/2 lens with focal length 40 mmmust have diameter 20 mm
f/2 lens with focal length 60 mmmust have diameter 30 mm
fnew = 60 mm
The first camera gives a wide-angle effect because the film is covered by an image that includes more than Alex
The longer camera gives a telephoto effect because Alex's image covers the entire film
the angle between the crossed yellow lines is smaller in the longer camera with the larger image!
The image stays in focus (sharp)
Wide angle and telephoto lenses work the same way
That's why telephoto lenses are long
They often have large diameters, to let in as much light as a normal lens would
smallerangleWide angle and telephoto effects in the pinhole camera only depend on the distance from pinhole to film