Some Questions and Answers about Camera Lenses

Your camera lens functions in much the same way as the lens of the human eye.
Basically, the lens collects light rays reflected from a subject and, unlike a
pinhole, focuses these rays to form a sharp image.

What makes a lens work?

A camera lens can be made from a piece of glass or plastic which has two
opposite regular surfaces, either both curved or one curved and the other flat.
Most camera lenses are actually made up of a number of lens "elements" which
function together and are simply referred to as a "lens".

As the light rays that are reflected from the subject pass through the camera
lens, they are bent. The extent to which they bend is controlled by the
composition of the lens and the curves of the lens surface. In a properly
designed lens, all the light rays from the same part of a subject will meet at
a point behind the lens. A sharp image of the subject is formed at the point
where these light rays meet. The film must be located at this point for the
picture to be in sharp focus.

What is the focal length of a lens and what does it do?

In very simple terms, focal length is the distance between the optical center
of the lens and the film when the lens is focused at infinity. The focal length
of the lens of most adjustable cameras is marked on the lens mount. The focal
length is usually given in millimetres or inches.

There is a direct relationship between the focal length of a lens and the image
size of the subject record ed on film: the longer the focal length, the larger
the image on the film. For example, if Lens A has a focal length of 50 mm, and
Lens B has a focal length of 150 mm. The subject is the same size and the same
distance from the lens in both situations.

In this case, the image produced by Lens B, which has a focal length of 150 mm,
is three times as large as the image produced by Lens A, which has a focal
length of 50 mm. A lens of long focal length produces a larger image than one
of short focal length.

What are lens openings, and how are they determined?

When we talk about a lens opening, we mean the opening (usually called
aperture) that lets the light through the lens to expose the film. The sizes of
lens openings are usu- ally expressed in terms of f-numbers, for example, 1/2.8
and f/4. The f-numbers are determined simply by dividing the focal length of
the lens by the diameter of the aperture.

For example, if the focal length of the lens is 100 mm and the aperture is 25
mm, the f-number is f/4 (100/25 = 4). So when you have a lens opening of 1/4,
you know that the aperture is only 1/4 of the focal length. Similarly, f/8
means that the aperture is 1/8 of the focal length, f/11 means the aperture is
1/11 th of the focal length, etc. When you understand that f-numbers indicate
the size of the aperture as a fraction of the focal length, it's easier to
understand that the smaller the f-number, the larger the lens opening.

Some typical f-numbers used in expressing a series of lens openings, from large
to small, are f/2, f/2.8, f/4, f/5.6, f/li, f/16, and f/22.

What does relative aperture mean?

Let's look at two lenses, each with a 9 mm aperture and focused on the same
person. Both lenses transmit the same amount of light, but Lens A has a focal
length of 50 mm and Lens B has a focal length of 150 mm. With the 150 mm lens,
the image of the subject produced on the film will be three times as large as
the image produced with the 50 mm lens. While both lenses transmit the same
amount of light reflected from the subject, the light is spread over an area
nine times as large with the 150 mm lens. For this reason the image made on the
film by the 150 mm lens is less bright. So while both lenses have a physical
aperture of 9 mm, the longer-focal-length lens has a smaller relative aperture.
It would be difficult to take properly exposed pictures if, for example, f/8 on
a long-focal-length lens and f/8 on a short focal length lens didn't mean the
same thing from an exposure point of view. Fortunately, they do but for this to
be true, the f/8 on the long focal length lens must be a physically larger
opening than the opening of f/8 on the shorter focal length lens. Both lenses
have the same _relative_ aperture but their _physical_ apertures are of
different sizes.

Why must I use a larger-than-normal lens opening when I use a lens-extension

For making extreme close-up pictures with some advanced cameras, you
can use an extension tube or bellows to extend the camera lens. These devices
allow you to get close to your subject and still get a sharp picture.

However, since the f-numbers on the camera are based on a normal lens-to-film
distance, the marked f-numbers are not a true indication of the image
brightness reaching the film when the lens-to-film distance is increased by a
lens- extension device. Since the image on the film is less bright when you use
a lens-extension device, you should make an exposure compensation by using a
larger lens opening or slower shutter speed. If your camera has a built-in
meter it will automatically indicate the correct exposure settings, no
additional compensation is necessary. If you're using a 35 mm camera without a
built-in meter, you can use the following table as a guide to determine the
amount of exposure increase necessary with an extended lens.
     Exposure Increase for Extended Lens 35 mm Cameras

Width of Subject Area   Open Lens by    Or Multiply Exposure
     (inches)               (f-stops)            Time by
       11                     1/3                  1.3
        5 1/8                 2/3                  1.6
        3 1/4                 1                    2
        2 1/4                 1 1/3                2.5
        2                     1 1/2                2.8
        1 1/4                 1 2/3                3.2
        1 1/8                 2                    4
        1                     2 1/2                5.7
          3/4                 3                    8

For cameras with built-in meters, use the exposure recommended by the meter.

What is depth of field?

The distance range within which objects in a picture look sharp is called depth
of field.

From a practical point of view. depth of field varies with the size of the lens
opening, the distance of the subject focused upon, and the focal length of the
lens. Depth of field becomes greater as

1. The size of the lens opening decreases.
2. The subject distance increases.
3. The focal length of the lens decreases (and subject distance remains

What is an aspheric lens?

The surface of the majority of lenses made today is a segment of a sphere. An
aspheric lens, on the other hand, has a curved surface which is not part of a
sphere. Aspheric lenses are more difficult to manufacture than normal lenses
and are not as common.

An aspheric lens will correct various lens aberrations that would ordinarily
require several more lens elements to correct. In addition to having fewer
elements, a lens with an aspheric element is lighter and usually more expensive
than a normal lens.

What Is a color-corrected lens?

A color-corrected lens is one that brings light rays of different colors
reflected from the same part of the subject into focus at the same point behind
the lens. A short history lesson will help you understand why color-corrected
lenses are important.

At one time, only black-and-white film was available. At first, black-
and-white film was sensitive only to blue light. Later it was orthochromatic,
that is, sensitive to both blue and green light. With many of the lenses used
at that time, light rays of different colors that came from the same part of
the subject did not come to focus at the same point behind the lens. But as
long as the film could see only blue and green light, it didnÕt make too much
diffeence when red light rays didnÕt come to focus at the same point as the
blue and the green light rays.

However, orthochromatic films weren't ideal. For example, since these films
couldn't see red light, red objects (like lips) registered as black on the
prints. For this reason, panchromatic films were developed. Because
panchromatic films are sensitive to all colors, they are capable of rendering
colors in proper degrees of black and gray. Now that the new films could see
red and other light rays, it was necessary to make a lens that would bring all
the light rays into focus at the same point.

Different lens formulas and different types of glass were developed to provide
proper, sharp register of all the light rays. These color-corrected lenses are
essential for color photography but were needed long before there was any such
thing as color film.

What is a coated lens?

A coated lens is one coated with a thin layer of special material that reduces
light reflections from the air-glass surfaces of the lens. Most photographic
lenses available today are coated.

LetÕs see what happens when the lens is uncoated. When light strikes any
air-glass surface of an uncoated lens, a small percentage of that light will
reflect back from the surface and not go through the lens. In a
multiple-element lens, each air-glass surface will reflect some of the
image-forming light that should reach the film. Most of this wasted light will
just be reflected from the surface back out through the front of the lens and
will be lost. However, some of these light rays may be reflected a second time
from the surface element of the lens so that they do reach the film. Because of
the several angles of reflection, such light rays will not reach the film at
the point where they should and will degrade the quality of the image.

Since the lens coating reduces the amount of light that is reflected from an
air-glass surface, it contributes to a clearer, crisper image and makes the
lens more efficient by reducing light loss.

If you look at a coated lens from an angle, the surface will appear colored.
However, the coating on a lens does not affect the color of pictures taken
through the lens. If you look through the lens, the coating is colorless.


m = magnification
F = focal length
F = f-number
x = distance of image from focal point or distance that
    lens is extended from infinity setting
u = subject distance
v = image distance
h = height of subject
hÕ= height of imag&

All dimensions must be expressed in the same unit of measure.
To convert dimension in        divide by

millimetres to metres       1000
centimetres to metres        100
inches to metres              39.4
feet to metres                 3.28
millimetres to inches         25.4

Measuring u and v from a point midway between the front element and the rear
element of the lens is accurate enough for practical use with a normal lens
(not telephoto or wide-angle). The formulas that do not include v are valid for
telephoto lenses and wide-angle lenses when u is large enough so that any
inaccuracy in measuring u from the center of the lens is insignificant.

The fundamental relationship between focal length, image distance, and subject
distance is

        1      1       1
        -  =   -   +   -
        F      v       u

Formulas that are more directly useful and some examples follow:


      hÕ    v      v-f    f
 M =  -  =  -  =  ---  = ---
      H     u      F     u-F

Lens-to-Image Distance:

 v = ----- = mu = (m+1)F

Subject-to-Image Distance:

          (m +1)squared
 u + v = --------------- F

Lens-to-Subject Distance:

      Fv      v   | 1     |
 u = ----  =  - = | - + 1 | F
      v-F     m   | m     |

Example 1: How long must a room be for you to photograph groups 10 feet wide
when you use a lens with a focal length of 8 inches on a 4 x 5 inch camera?

Solution: Allow 41/2 inches for image on horizontal axis of negative. Work in
inches, so 10 feet = 120 inches.

                   h'   4.5
 Then m =    ----- -  .038
                   h    120

         |  1      |
 and u = | --- + 1 | F =
         |.038     |

(26.3 + 1) F = 27.3 x 8 = 218 inches = 18+ feet

This answer gives the lens-to-subject distance. You will also need to add at
least 7 feet to allow space for the camera, photographer. background
separation, etc. The minimum room length is therefore 25 feet. The room width
must be at least 15 feet in order to accommodate the group and lights.

Focal Length:

       u             v
F = --------  =  ---------
    | 1     |      m + 1
    | - + 1 |
    | m     |

Example 2: For a room 20 x 32 feet and a 21/4 X 21/4 inch camera, what is the
longest focal-length lens feasible for photographing a scene 10 feet wide?

Solution: Since you need about 7 feet of room length for working space, the
maximum lens-to-subject distance available is 25 feet (32-7) or 300 inches; u =
300. You should allow at least 1/8 inch of space on either side of the
negative. The usable width of the negative is then 2 inches. Since the width of
the subject is 10 feet (120 inches), the magnification (m) equals 2 divided by
120, or .017 The formula now reads:

        300             300
 F = -----------  =  --------   =
      1/.017 + 1      59 + 1

 --- = 5

Answer: 5 inches (127 mm) is the maximum usable focal length.

Lens Movement from Infinity Position:

     F squared
x =  ---------
       u - F

Field Size (front-element focusing lenses):
Field width = negative width x ---

Effective f-Number for Lens Extension:

The effective f-number is greater than the indicated f-number because of the
increased image distance (lens-to-film distance). When the subject distance u
is less than 8 times the focal length of the camera lens, use one of the
following formulas to determine the required exposure compensation. The
formulas are valid for any subject distance.

                                  v x f
        Effective f-number =     ------- = f (m + 1)

Where v = lens-to-film distance or focal length plus lens extension from
infinity focus, f = f-number indicated on lens-opening scale and F = focal
length. For close-up pictures with lens extension, use the effective f-number
obtained from the first formula when determining your exposure, or compensate
your exposure time directly by using the second formula.

Note: Exposure compensation is made automatically with some cameras through
the lens exposure meters. Correction may or may not be necessary with flash.

                        Fixed Circle of Confusion
Camera                  Most Widely Used (in inches)

8 mm movie                     .0005
Super 8 movie                  .00065
16 mm movie                    .001
110 (13 X 17 mm)               .0012
126 (28 x 28 mm)               .002
135 (24 X 36 mm)               .002
Roll film                      .005
4 x 5-inch and          F/1720 critical use
    larger           or F/10OO liberal use


Depth-of-field computations are made on the basis of a fixed circle of
confusion or on a circle of confusion equal to a fraction of the focal length.
Lenses of different focal lengths used at the same f-number have the same depth
of field for equal image sizes. As a general rule, one-third of the depth of
field is in front of the subject and two-thirds is behind the subject. An
exception to this rule is extreme close-up lenses, including those made with
close-up lenses, where depth of field is about equal on both sides of the

Method A, Fixed Circle of Confusion:

F = focal length of lens
f = f-number setting
H = hyperfocal distance
u = distance for which camera is focused
d = diameter of circle of confusion
                                                             H x u
Near limit of depth of field (measured from camera lens) = ----------
                                                            H + (u-F)

                                                              H x u
Far limit of depth of field (measured from camera lens)  = ----------
                                                            H - (u-F)

Hyperfocal Distance (near limit of depth of field when lens is set at infinity):

      F squared
H=  -------------
       f x d

Method B, Circle of Confusion a Fraction of the Focal Length of the Lens:

u = distance focused upon.
0 = angular size of circle of confusion. For critical definition, 0 is 2 minutes
of arc and the linear size of the circle of confusion is approximately F/1720
(tan 2Õ=.00058).

L =  effective diameter of lens = ---

LDF = limit of depth of field

                                              u squared  tan 0
Near LDF: (measured from plane focused on) = -----------------
                                               L + u tan 0

                                              u squared  tan 0
Far LDF: (measured from plane focused on)  = -----------------
                                               L - u tan 0