Camera and Lens

Photography Fundamentals

Course 1 · Chapter 2 · Camera and Lens: Focal Length, Angle of View, Sensor Size

Focal Length and Angle of View

Photography Fundamentals 1 covered how much light reaches the sensor. This chapter covers how much of the scene the lens takes in. The lens's focal length, together with the size of the sensor, sets the angle of view. A shorter focal length gives a wider angle and a longer one a narrower angle.

Wikipedia's Angle of view article gives the formula α = 2 arctan(d / 2f), where d is the sensor dimension being measured (width, height or diagonal) and f is the focal length. The script below applies it to a 36 by 24 mm sensor (the "35 mm full frame" size, diagonal 43.3 mm) and I ran it to get the output shown.

from math import atan, degrees, hypot

def angle(d, f):
    return degrees(2 * atan(d / (2 * f)))

W, H = 36, 24
diag = hypot(W, H)
print(f"diagonal {diag:.1f} mm")
for f in (24, 35, 50, 85, 200):
    print(f"{f} mm: horizontal {angle(W, f):.1f}, diagonal {angle(diag, f):.1f}")
crop = diag / hypot(23.7, 15.6)
print(f"APS-C crop factor {crop:.2f}; 50 mm equals {50 * crop:.0f} mm")

# Output
diagonal 43.3 mm
24 mm: horizontal 73.7, diagonal 84.1
35 mm: horizontal 54.4, diagonal 63.4
50 mm: horizontal 39.6, diagonal 46.8
85 mm: horizontal 23.9, diagonal 28.6
200 mm: horizontal 10.3, diagonal 12.3
APS-C crop factor 1.52; 50 mm equals 76 mm

The 50 mm line matches the article's own worked example (39.6, 27.0 vertical and 46.8 degrees diagonal).

Lens Types by Focal Length

The Normal lens article says a lens whose focal length is close to the frame diagonal (about 43 mm on full frame) gives a "natural" view; 50 mm is the most common choice, and roughly 40 to 58 mm counts as normal. Shorter is wide-angle, longer is telephoto (a common kind of long-focus lens). The Angle of view article groups them by diagonal angle:

Type	Focal length (full frame)	Diagonal angle
Wide-angle	24 to 35 mm	about 84 to 64 degrees
Standard	36 to 60 mm	about 62 to 40 degrees
Medium telephoto	85 to 250 mm	about 30 to 10 degrees
Super telephoto	over 300 mm	under 8 degrees

Check your numbers against the table

The script gives 84.1 degrees for 24 mm, 63.4 for 35 mm, 28.6 for 85 mm and 12.3 for 200 mm, all inside the table's ranges. The ranges are descriptive groupings from one article, not an official standard (check).

Sensor Size and the Crop Factor

A smaller sensor sees a narrower slice of what the lens projects, so the same lens gives a narrower angle. The Crop factor article defines the crop factor as the 35 mm frame diagonal (43.3 mm) divided by the sensor diagonal. Multiply the focal length by it to get the full-frame focal length with the same field of view. The lens's real focal length does not change.

Format	Sensor (mm)	Crop factor
Full frame 35 mm	36 by 24	1.0
Canon APS-C	22.2 by 14.8	1.6
General APS-C (Nikon DX, Sony, Fujifilm X and others)	23.7 by 15.6	1.5
4/3" Four Thirds	17.3 by 13.0	2

Equivalent is about the view, not the light

The factor describes field of view only. The article's example is a 50 mm lens on a 1.6 times sensor framing like an 80 mm on full frame. It does not mean the lens "becomes" an 80 mm in any other respect. How sensor size affects depth of field and noise is outside this chapter (check).

Prime and Zoom

A prime lens has one fixed focal length; a zoom covers a range. These two terms are standard photography vocabulary, but I did not check a source for them in this session (check). A practical point from Chapter 1: lenses are also described by their widest aperture (for example f/1.8 or f/2.8), the lowest f-number they allow, which sets how much light they can gather.

Not Yet Verified, and Sources

Sources. Wikipedia articles Angle of view (photography), Normal lens and Crop factor. Each answer was read through a page summary, not the full text, so details beyond what is quoted here were not seen.
Not in those pages. The definitions of prime and zoom, the effect of sensor size on depth of field and noise, and whether the handheld rule should use actual or equivalent focal length (all check).
Conflict to note. The Crop factor page lists Canon APS-C as 1.6 and other APS-C as 1.5; my script's 1.52 uses the 23.7 by 15.6 mm size. Both figures are right for their sensors.

Exercises

Exercise 1

Edit the script to find the horizontal angle of a 35 mm lens on full frame (36 mm wide) and on a 23.7 mm wide APS-C sensor. Which is wider, and what full-frame focal length does the APS-C view match, using the crop factor?

→ Solution

Exercise 2

Using the script and the lens-type table, compute the diagonal angle for 24, 50, 85 and 300 mm on full frame and name the type each falls into.

→ Solution

Exercise 3

A 200 mm lens is fitted to a Four Thirds camera (crop factor 2). What full-frame focal length does it match for field of view? Then apply Chapter 1's handheld rule of thumb to the lens's actual focal length and name the shutter speed from the standard series. State one thing you are unsure of.

→ Solution

Quick Reference

Angle of view: 2 arctan(d / 2f)
Normal lens: about 43 mm on full frame; 50 mm common
Crop factor: 43.3 mm divided by the sensor diagonal
Values: APS-C 1.5 (Canon 1.6), Four Thirds 2
Check: prime and zoom definitions, sensor size effects beyond view

Coming next

Photography Fundamentals 3 takes up depth of field and focus, which bring Chapter 1's aperture together with this chapter's focal length.