Perspective problem

Lynnzer

New member
Joined
Jan 14, 2020
Messages
1
Been a long time since schooldays, 60 odd years to be frank.
Anyway, I have a problem with trying to figure out how large an object of 1cm would appear to someone who is 9.2 metres away from it.
This relates to the size of text on a car park sign where the text is only a centimetre high and driver is passing by at a distance of 9.2 metres.
I have a belief that the text would be so small as to make it unreadable. I really do need an answer on this though so if anyone can assist I'd appreciate it, however if a formula of sorts can be given I may be able to work it out myself.
Many thanks
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
19,987
Been a long time since schooldays, 60 odd years to be frank.
Anyway, I have a problem with trying to figure out how large an object of 1cm would appear to someone who is 9.2 metres away from it.
This relates to the size of text on a car park sign where the text is only a centimetre high and driver is passing by at a distance of 9.2 metres.
I have a belief that the text would be so small as to make it unreadable. I really do need an answer on this though so if anyone can assist I'd appreciate it, however if a formula of sorts can be given I may be able to work it out myself.
Many thanks
My advice would be for you go to an optician's store/office and use their eye-chart to directly measure. The answer would depend on the "optical" age of the eye of the beholder.
 

lev888

Full Member
Joined
Jan 16, 2018
Messages
875
Been a long time since schooldays, 60 odd years to be frank.
Anyway, I have a problem with trying to figure out how large an object of 1cm would appear to someone who is 9.2 metres away from it.
This relates to the size of text on a car park sign where the text is only a centimetre high and driver is passing by at a distance of 9.2 metres.
I have a belief that the text would be so small as to make it unreadable. I really do need an answer on this though so if anyone can assist I'd appreciate it, however if a formula of sorts can be given I may be able to work it out myself.
Many thanks
Find 1cm text (newspaper, cereal box, etc). Stand 9.2 metres away, read. Not sure what you are trying to calculate.
 

Mr. Bland

Junior Member
Joined
Dec 27, 2019
Messages
90
The best solution to your exact problem is probably as others have stated: experiment and see how it looks. If that's not an option, there are likely accessibility guidelines you can consult to find out what researchers have determined regarding how large text "should" be at a given distance.

Mathematically, perspective is a form of projection that is most commonly used to transform coordinates in \(\displaystyle n\) dimensions into coordinates in \(\displaystyle n - 1\) dimensions (such as 3D to 2D for display on a TV or computer monitor). This process requires a surface of sorts to project onto, which must be larger than a point. If the observer is a point, then all coordinates in the viewing space get projected to the same position and will not produce a useful result. For this reason, the question "how large is an object \(\displaystyle x\) units away" can't be answered, as the target region isn't defined.

In human terms, the target of the projection is the retina inside the eye, and the field of view is determined by the lens and pupil. I don't have the numbers for that on me, so once again, consult the accessibility guidelines.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
6,005
Let's compare your text to the Snellen chart!

There we find that the 6/6 line (20/20 in the US) subtends 5 arcminutes, which (at 6 meters) is 8.73 mm tall; the 6/12 (20/40) line (which marks the visual acuity expected of a driver in the US) is twice as tall, or about 17.46 mm = 1.746 cm.

At 9.2 m, you should be able to read a letter that is 9.2/6*1.746 = 2.677 cm high.

So a driver is not expected to be able to read a letter 1 cm high! One caveat is that the letters on a Snellen chart are not in a normal font; I'm not sure whether whatever font was on the sign would be more or less readable than the Snellen's "optotype". (I'd never heard of that!) Also, if this is for a court case, you should check the laws of your country to see what level of vision is legal for driving. There might also be laws specifying size of type on signs for particular purposes.
 
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