Together with the camera body, the photographic lens is the fundamental element of a photographic system which allows us to transform our artistic and creative vision into a photograph.

Inside the *barrel*, the external part of the lens, there are a series of lenses also called *elements* which are organized into *groups* whose number, type and arrangement change according to the optical scheme of the lens and design choices.

Made of very high quality glass and exploiting the laws of optical physics, these lenses allow for focus, i.e. to convey the light rays of a part of the space onto the sensor, determining its focal length.

### FOCAL LENGTH

If a lens were composed of a single lens, the focal length would be the distance (in mm), between the center of the lens and the focal plane, where the digital sensor is positioned.

However, considering that lenses are never composed of a single lens but have multiple optical elements inside them, the focal length of a lens is called the *optical center* or *rear nodal point.* This is generally located near the diaphragm and it is calculated mathematically according to the individual lenses present in the system.

This is why lenses with similar focal lengths also have very different physical dimensions. Lenses with shorter focal lengths than others can be physically larger. In zoom lenses, by means of a ring placed on the barrel, it is possible to move certain groups of lenses which then modify the distance of the optical center with respect to the focal plane, consequently changing the focal length.

### ANGLE OF VIEW

The lens’ **angle of view** is an aspect directly related to the focal length.

Mathematically it is **the angle measured at the vertex of an isosceles triangle placed on the axis of the focal plane of the lens with the size of the image formed on the diagonal of the sensor at the base and the lens focused at infinity**.

If the focal length is a nominal datum and related to the dioptric power of the lens, the angle of view instead depends on the dimensions of the frame (film or sensor), which determine at least three angles of the framed field: horizontal, vertical and diagonal .

Regardless of the aspect ratio (1:1, 4:3, 3:2, 16:9, etc.), the diagonal measurement is always equivalent to the measurement of the diameter of the circumference which precisely circumscribes the frame, but for practical use in photography it could be more useful to know the horizontal shooting angle of the frame or for example in Cinema and TV the vertical measurement is also used for various reasons (anamorphic optics, height of the subjects, etc.).

Trigonometry can be used to calculate degrees of camera angle, with respect to one of the three known dimensions of the frame (height, width, or diagonal).

Conventionally, for a rectilinear optic (not fish-eye) with focal length **f** and a diagonal recording medium **d**, the angle (in degrees) is defined as:

\alpha_d = \dfrac{360}{\pi} arcotan \dfrac{d}{2f}

Being a trigonometric function, the angle of view does not vary linearly with the reciprocal of the focal length, but in any case, for telescopic optics it can be approximated in

{\alpha \approx {\dfrac {d}{f}}} \quad radians

or

{{\dfrac {180d}{\pi f}}} \quad degrees

The focal length must also be changed if the distance from the subject is comparable to the focal length, i.e. in the case of macro or micro photography. In that case the magnification factor has to be considered

{f=F(1+m)}{f=F(1+m)}

A 90mm focal length lens, used on a 24x36mm sensor camera and focused to infinity, produces the following angles of view:

{\alpha _{c}={\dfrac {360}{\pi }}arctan {\dfrac {24}{2\times 90}}\approx 15,2^{\circ }}\alpha _{c}={\dfrac {360}{\pi }}arctan {\dfrac {24}{2\times 90}}\approx 15,2^{\circ }

{\alpha _{l}={\dfrac {360}{\pi }}arctan {\dfrac {36}{2\times 90}}\approx 22,6^{\circ }}\alpha _{l}={\dfrac {360}{\pi }}arctan {\dfrac {36}{2\times 90}}\approx 22,6^{\circ }

{\alpha _{d}={\dfrac {360}{\pi }}arctan {\dfrac {43,3}{2\times 90}}\approx 27^{\circ }}\alpha _{d}={\dfrac {360}{\pi }}arctan {\dfrac {43,3}{2\times 90}}\approx 27^{\circ }

The angle of view in relation to the format for the classification of the lenses is a relative and not an absolute parameter as is the focal length and, for photo-cinematographic purposes, based on the diagonal, seven types of lenses can be roughly distinguished:

SUPER TELEPHOTO

(with angle of view up to 8°)

TELEPHOTO

(with angle of view up to 25°)

MEDIUM TELEPHOTO

(with angle of view up to 50°)

STANDARD

(with angle of view up to 60, exactlydi 53°)

WIDE ANGLE

(with angle of view up to90°)

SUPER WIDE ANGLE

(with angle of view up to 110°)

ULTRA WIDE ANGLE

(with angle of view up to 110°)

For the same sensor size, lenses with a shorter focal length have a wider angle of view. Lenses with a longer focal length have a smaller angle of view. A greater angle of view translates into more things that can fit into the frame.

### CROP FACTOR

What has been described above, in relation to the variation of the angle of view, assumes a fixed size of the sensor and a variable focal length.

Now let’s assume we take a fixed focal length into consideration and decrease the sensor size.

Reducing the dimensions of the sensor, with the same focal length, geometrically implies reducing the base of the triangle placed on the focal plane, and consequently of having a narrower angle of view. Conversely, increasing the dimensions of the sensor, with the same focal length, implies increasing the base of the triangle placed on the focal plane and consequently of having a wider angle of view.

The crop factor indicates the ratio between the diagonal of a traditional full-frame sensor and the diagonal of a smaller sensor. The term crop refers to the fact that a smaller sensor records, other things being equal, an image that corresponds to an internal portion (a crop) of what would be recorded by a larger sensor.

Cameras that have a sensor size as a 35mm negative (crop factor = 1) are called full-frame; cameras that have a sensor size smaller than a 35mm negative (crop factor > 1) are smaller formats than full frame.

In medium format cameras, having a sensor larger than full frame, the crop factor is <1.
[/av_textblock]
[av_hr class='invisible' icon_select='yes' icon='ue808' font='entypo-fontello' position='center' shadow='no-shadow' height='50' custom_border='av-border-thin' custom_width='50px' custom_margin_top='30px' custom_margin_bottom='30px' custom_border_color='' custom_icon_color='' id='' custom_class='' template_class='' av_uid='av-3jiei4' sc_version='1.0' admin_preview_bg='']
[av_textblock textblock_styling_align='' textblock_styling='' textblock_styling_gap='' textblock_styling_mobile='' size='16' av-desktop-font-size='' av-medium-font-size='' av-small-font-size='' av-mini-font-size='' font_color='custom' color='#f8f8f8' id='' custom_class='' template_class='' av_uid='av-lbzfzivp' sc_version='1.0' admin_preview_bg='']

**Some examples of crop factor**

Camera | Sensor | Diagonal | Crop |
---|---|---|---|

Phase One IQ4 | 40mm x 53,4mm | 66,720mm | 0,648 |

Hasselblad X2D | 33mm x 44mm | 55mm | 0,786 |

Fuji GFX 100s | 32,9mm x 43,8mm | 54,780mm | 0,789 |

Leica S2 | 30mm x 45mm | 54,083mm | 0,800 |

Leica SL2 | 24mm x 36mm | 43,267mm | 1 |

APS-H/td> | 18,6mm x 27,9mm | 33,531mm | 1,290 |

APS-C | 15,6mm x 23,5mm | 28,206mm | 1,533 |

Canon APS-C | 19,9mm x 22,3mm | 26,819mm | 1,613 |

**Practical implications of the crop factor**

Based on what has been said above, for example, the angle of view of a 50 mm (native full frame), mounted on APS-C , corresponds to the angle of view of a 75 mm (native full frame) on full frame and an angle of view of a 100 mm (native full frame) on full frame when mounted on a 4:3 micro.

In regards to the images produced, it should be noted that the depth of field, depending on the real focal length of the lens and the distance from the subject, would still be that of a 50 mm. Using native focal lengths for a given format on different formats determines the variation of the original field angle characteristic of the format for which the lens was designed, therefore a narrower or wider framing.

To compensate for the difference in the angle of view generated when switching from one format to another, in other words to have the same frame width, it is possible to increase or decrease the distance from the subject but not without significant variations in the depth of field.