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I'm trying to understand the FOV range for a Canon 18-55 lens. The datasheet gives the following for diagonal angle of view:

Diagonal Angle of View: 74°20'–27°50"

How do I read this? Is it 74.2 degrees to 27.5 degrees? What are the apostrophes/quotes that I'd normally associate with feet/inches doing here?

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    \$\begingroup\$ I’m voting to close this question because it's not about photography, it's about fundamental mathematics. \$\endgroup\$
    – osullic
    Mar 5, 2023 at 20:00
  • \$\begingroup\$ Fair @osullic, obviously I didn't know whether it was generalized math or some photography specific thing. I took high school trig but that was 15 years ago, I do not remember learning this. Consider that maybe others might come to photography specific Q&A board for this same answer as this notation seems common for photography specifications specifically (I normally read spec sheets for all sorts of hardware and haven't happened to encounter degree notation anywhere else before). \$\endgroup\$
    – A__
    Mar 6, 2023 at 16:16
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    \$\begingroup\$ It's certainly an elementary question, and for the most part, I agree it's not normally on-topic for Photo-SE. But OP's question arose from reading a lens's spec sheet (a pretty common consumer lens at that). It's reasonable to ask how to interpret numbers or dimensions on a lens spec that they might not be familiar with reading. \$\endgroup\$
    – scottbb
    Mar 6, 2023 at 19:08
  • \$\begingroup\$ I know it's a small leap, but for me it's not much different to someone asking "what is a millimetre?" because they saw it in a focal length specification. The reason degrees, minutes and seconds are used in specifications is because it's taken as given that readers know what these mean. My high school maths days are a fair bit more than 15 years ago, and this still seems fundamental to me. Also, in fairness, it does seem like there wasn't even a cursory web search performed before asking. \$\endgroup\$
    – osullic
    Mar 6, 2023 at 23:20
  • \$\begingroup\$ @osullic Fair enough, I agree with you. My bad. I did do a cursory web search. I would never waste the lengthy amount of time it takes to craft a passable stackexchange post before doing at least a few minutes searching. Famously-- making the post often triggers the obviousness immediately in retrospect, right. Anyway, I did get my answer. Beautifully detailed answers, even. Feel free to nuke this. \$\endgroup\$
    – A__
    Mar 7, 2023 at 2:54

4 Answers 4

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This is the standard minute and second of arc notation for fractions of a degree; one minute (′) is 1/60th of a degree and one second (″) is 1/60th of a minute.

(I am slightly suspicious that the second angle is a typo and it should be 27°50′ but that's mostly irrelevant here)

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In trigonometry, degrees are subdivided into 60 minutes (indicated with a single quote or apostrophe). Each minute is further subdivided into 60 seconds (indicated with a double quote). So 74 degrees and 20 minutes is 74.3333 degrees. 27 degrees and 50 seconds is 27.0138888 degrees.

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All of the other answers are correct. This one is just adding some pedantic history to the context of minutes and seconds.

  • In both time and angular measurements (which are pretty intricately linked by the earth's mean apparent rotation rate (solar or synodic day), the Latin terms for the subdivisions of the degree (angular) and hour (time) are partes minutae primae, 'primary minute part'; and partes minutiae secundae, secondary minute part (where 'minute' [IPA: /maɪˈnjuːt/, "my NEWT"] means minutiae: 'tiny', 'small'). That is,
    • the first (primary) division of degrees/hours is the minutiae (i.e., 'minute'); and
    • the second (secondary) division of degrees/hours is the secondary minutiae, or just second.
  • The prime ( ) and double prime ( ) marks symbolically represent the 'first cut' (or 'first measurement') and 'second cut' ('secondary measurement'). But be careful, don't over-analyze or over-systematize this too much. Compare the following dimension measurements:
    • Time: hh Hours, mm Minutes, ss Seconds: hh:mm:ss, hh mm' ss"
    • Angular: dd Degrees, mm Minutes, ss Seconds: dddº mm' ss"
    • Distance: ... ? larger measurement (yard, furlong, cubit, etc.), ff Feet, ii Inches: ...? ff' ii"
  • The sexagesimal (base-60) divisions of minutes and seconds (and relatedly, 360º angular division) are historically due to the Babylonian base-60 number system. In antiquity, real numbers weren't a formalized concept. Numbers were either whole numbers (1, 2, 3, ...) or rational whole number parts (fractions, 1/3, 2/5, etc.) of a whole number. Base-60 is very convenient as a means of partial/fractional counting because its primary divisors are 3, 4, and 5 (that is, 3 * 4 * 5 = 60), consisting of the smallest whole numbers (including 2, which is part of any even number like 4). Antiquity had not developed a positional number system, so easy computation with small integers, or multiples of them, was beneficial.
  • Ultimately, both the angular and time measurement divisions into hours/degrees, minutes and seconds, is unified by astronomy. Because the earth's rotation is relatively constant (certainly over a human's observational lifetime), the angular velocity of the stars through the nighttime sky is constant. Without going into the history of the division of day and night into 12 hours (which, due to seasonal variation, are not constant durations), note that a day's rotation of 24 hours equates to 360º of rotation; thus, 1 hour is 360º/24h = 15º of the sun's (or stars) travel; 1 time minute is 15 arcminutes of celestial travel; 1 time second is 15 arcseconds of celestial travel.
    • The moon and sun: both the moon and sun are very close to 0.5º of arc (30 arcminutes) wide. Coincidentally, the end of your little finger at arm's length covers about 1º of arc, and your pinky's fingernail is about 1/2º wide, or approximately the moon or sun diameter in the sky.
    • Therefore, it takes the moon and the sun about 2 minutes of time (120 seconds) to travel their own diameter (aobut 1 pinky nail width) across the sky. Said another way, if you could hold your arm and hand perfectly still for several minutes, if the sun/moon were just obscured by one edge of your pinky finger at full extension, it would take about 4 minutes before the other edge of the sun/moon became visible on the other side of your pinky.
    • ... and other convenient rules of thumb (pinky?) can be calculated and applied. (note: this astronomical rule of thumb does not appear to have any historical basis for the term 'rule of thumb') (nor does the aprocryphal rule pertaining to the size of switch a man may beat his wife with; please don't propagate that false rule).
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degree˚, minute' (1/60th of ˚), seconds" (1/60th of ').

At 18mm the DAOV is 74 degrees and 20 minutes; at 55mm it is 27 degrees and 55 seconds(not quite 1 minute).

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