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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:

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

Exposure

Physics 1230: LightandColorChapter 4blocked raysA pinhole camera works by blocking rays

- What is an image?
- A real image is formed on a screen when rays from each point on the object reach the corresponding points on the screen and no other rays from other points on the object reach those points

Pinhole Camera

Image oflight bulb

Light bulb

blocked raysThe object photographed with a pinhole camera does not have to be self-luminous!

One of many rays of light shining on Alex

Pinhole Camera

Rays from the real Alex go through the hole

and make the image

Image ofAlex

Alex

Why we do not use such a simple camera?

- (A) Not very bright images;
- (B) Focusing is difficult;
- (C) Because of spherical aberrations;
- (D) A, B, & C
- (E) none of the above;

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

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

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

A telephoto effect (enlarged image) for a pinhole camera only requires increasing the distance from pinhole to camera backAs 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

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

f

f

fnew

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

For most of us these days a zoom lens is used whose focal length can be adjusted and changed

Advanced photographers use interchangeable lenses with different focal lengths for different effects

A telephoto effect is achieved in cameras in a variety of ways- The distance, xi, from the lens to the back of the camera must be adjusted for each different focal length
- xi must = that special distance at which rays from an object point all come together (intersect) at image point
- This is called focusing
- For other distances, xi, the image at the camera back is said to be out of focus
- Interact with the lens

Back of camera where film or CCD (for digital camera) goes

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 cameraThe depth of focus is the range of lens to camera-back positions at which the image is tolerably sharp (in focus)

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

f

circles ofconfusion

f

missing ray

smallercircle ofconfusion

What is the depth of focus of a lens in a camera?Depth of field is related to depth of focus

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

Depth offield

diameter of

circle of confusion(maximum tolerable blur)

What is the depth of field of a lens?The diameter of the aperture of a lens can be reduced by means of the diaphragm.

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?

10

5

40 mm focallength lens

at full apertureof diameter

d = 10 mm

40 mm focallength lens

with apertureof diameterd = 5 mm

What are apertures, f-numbers and stops?40

f

= 4 ( = f/4)

f-number =

10

d

a) f/2, b) f/4, c) f/6, d) f/8, e) f/10

Exam # 1 was & extra credit assignments

- A. Trivial
- B. Relatively easy;
- C. Appropriate;
- D. Difficult;
- E. Overwhelmingly difficult;

- A. I will do extra credit projects to improve my grade (20points/project);
- B. I will not do extra credit projects;

single lens reflex (SLR) is most folks' idea of a serious camera. SLR means

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.

is the symbol which means proportional to

A d2 means A = const·d2

If d is doubled A increases by a factor of 4 no matter what the constant is!!

Example

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:

A d2

Double d by multiplying by 2

Note (2d)2 = 4d2 so the new area is 4 times the old area.

Mini-lesson on proportionalityThe volume, V, of a spherical balloon is proportional to its diameter, d, cubed:

V d3

If the diameter is doubled by how much does the volume change?

a factor 2

a factor 4

a factor 6

a factor 8

Answer:

(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

d √A

If the area is made 4 times larger, by what factor is the diameter increased?

b) √2, c) 4

Ans: √(4A) = √4·√A = 2·√A

Practice questionsA larger aperture lens brings more rays from each point on the object to the corresponding point on the image

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)Pinhole

Small aperture lens

Large aperture lens

with samefocal length

as smaller aperture lens

Light energy Lens area

Area, A, of lens is proportional to lens diameter, d, squared

A d2

Therefore, lens diameter, d, is proportional to square root of lens area

d √A

Double the area and d increases by what factor?

√2

2

4

Lens

d

diameter of lens = d

Light energy reaching film each second is proportional totheAREA of lensCamera

Area of lens = A = π(d/2)2

f-stop = (focal length)/d

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

5

10

5·√2

40 mm focallength lens

with apertureof diameterd = 5 mm

40 mm lens

at full apertureof diameter

2d = 10 mm

More light energy reaches the film when the f-stop of the lens is decreasednew diameter= √2·d mm

= 7.1 mm

40/(√2·d)= f/5.6

40/(2d)= f/4

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)

f/22

f/16

f/11

f/8

f/5.6

f/4

f/2.8

f/2

f/1.4

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 secSmallerf-stops

Depth of field video

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 the CCD at the back of a camera when the shutter is left open longer

Image gets brighter if shutter is left open longer

A light wave continues to deliver energy as long as the wave keeps moving into an eye or a lens1/15 sec

1/30 sec

1/60 sec

1/125 sec

1/250 sec

1/500 sec

1/1000 sec

1/2000 sec

Sequence of shutter speeds in which each faster speed lets in half the light energyFaster speeds, better able tostop (freeze) fast motionbut give darker image

The exposure of film (or a CCD) is proportional to the total amount oflight energy falling on the film (or CCD) during the time the shutter is left open

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 open

What is meant by exposure of a picture?f/22

f/16

f/11

f/8

f/5.6

f/4

f/2.8

f/2

f/1.4

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

Equivalent combinations of f/stops and shutter speeds (which deliver the same energy to the film or CCD). All give sameexposure!- 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

Intensity of light is defined as energy per second per unit area

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?

r

Light is more intense when there is more energy per unit area.Light

bulb

Draw an imaginary sphere whose radius, r is thedistance from your eye to the center of the light bulb

- The intensity of light is the same everywhere on the sphere and equal to the power divided by the area of the sphere

The area of the sphere is proportional to r2 so the intensityis proportional to 1/r2

Intensity of light is energy per second per unit area

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.Why is f-number = f/d?

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).

20 mm

f = 40 mm

30 mm

fnew = 60 mm

Why 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

If the 60 mm lens did not have a larger diameter than the 40 mm lens, the intensity of the larger image would be

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 intensity

We can prove that two lenses with the same f-number give an image of Alex with the same light intensity20 mm

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

30 mm

fnew = 60 mm

As the distance between the pinhole and the back of the pinhole camera is increased the image increases in size

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

Film

covers

back of

camera

smallerangle

Wide angle and telephoto effects in the pinhole camera only depend on the distance from pinhole to filmFor photography of objects at different distances from us we use

- A. Camera with CCD that has at least 5 megapixels;
- B. Small aperture (large f-number);
- C. Large aperture (small f-number);
- D. Short exposure;
- E. A, B, C, & D

For photography of moving objects we use

- A. Camera with CCD that has at least 5 megapixels;
- B. Small aperture (large f-number);
- C. Large aperture (small f-number);
- D. Short exposure and larger aperture;
- E. A, B, C, & D

Extra credit questions

- What settings we use for small depth of field?
- What settings we use to make photos late in the evening (not much light)?
- What would you do to make a photo during a very sunny day?
- Explain how the photo on the left was done

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