Physics - Optics: Circular Aperture - Angle of Resolution (3 of 6) Resolution Power of the Human Eye

[@RayleighCriterion]

That was very generous on the Angular Resolution of human vision, going down just 31½ arc seconds, which I doubt anyone has such good vision. Most people are limited to about 60 arc seconds and a very small percentage with excellent vision might achieve 40 arc seconds, these would be a person who can score 20/10 on the Snellen vision chart.

[@MichelvanBiezen]

Great input to this concept. 🙂

[@amosgabrielodhiamboamosowi726]

Your explanations are very clear. Thanks for sharing.

[@MichelvanBiezen]

You are welcome!

[@erezshidlov5294]

Hi, I have a question: You arrived at the formula for Theta, for the diffraction pattern on the screen/retina, but when you look at the light sources (like the hair or the moon crater) it's on the other side of the lens/aperture, and I don't understand why does the formula apply for the source side. Who guarantees that when 2 Airy discs don't overlap on the source side, they don't overlap on the screen/retina side ? I understand that there is a light source vs screen symmetry here (that is to say they are inter-changable), but aren't we assuming that we get a diffraction pattern on one side because we have a point source on the other side ? (The Airy disc is usually derived assuming planar waves arriving the aperture/lens) Thanks a lot !!! Very good and informative videos ! helped me a lot, keep up the fruitful work !

[@ravindranegi7360]

Even I have the same doubt. I cant find the answer to this question anywhere😔

[@manueljenkin95]

In the earlier case there was no lens. In this case there is a lens focussing the image. In the Fourier model of lens, a lens will convert objects input angle (the angle made by light from the two sources passing through the optic axis) to output position on the screen (our eyes will do it on the retina). This final output position formed on the retina hence corresponds to the input angle subtended by the objects.

[@spandansreyanshupadhee]

You are legit god for me sir

[@MichelvanBiezen]

Thank you! 😃

[@don_wild]

It's theoretical limit of eye's resolution, right? Otherwise, how can you explain known fact that birds of prey have a much better sight than humans, while having a smaller pupil size?

[@MichelvanBiezen]

It turns out that birds of pray have very large pupils which allows them to see small animals from very high.

[@jonahansen]

I think he's calculating the diffraction limit at the eye, but actually detecting that depends on the eye anatomy, essentially the spacing of photoreceptors on the retina. For humans, this is about the value Michel gets since cones are spaced about 2.5 um apart, but I would assume eagles have a much closer spacing.

[@josealejandrovelasquezcast3471]

Trying to folow your algebra. And I note that Its necesary to take the inverse of sin to obtain the angle. Why didn't you do it ? Ohh It's for the paraxial aproximation right ? sin x aprox x

[@MichelvanBiezen]

Yes indeed (for small angles)

[@jonahansen]

Michel - I'm not sure you are calculating the resolution of the human eye here. You are calculating the diffraction limit AT the eye for object at different distances, assuming that the eye can detect down to the diffraction limit. It's an empirical question how well the eye can resolve separate points, and must depend on the spacing of the receptors in the eye. And in the fovea, that would be cones for color vision - which are larger than rods so less resolution (and sensitivity) than for slightly off center vision. As it turns out, the foveal cones are about 2.5 um apart, and the optical center is 17 mm from the retina, giving a tan(theta) of 1.47x10-4, so you happen to be right serendipitously as this is about the diffraction limit.

[@shaunkiya]

Sir what would be the effect of using spectacles on resolution formula . How to calculate please tell ..

[@MichelvanBiezen]

if the spectacles increase the image size and therefore the apparent angles, then they could improve the angle of resolution

[@OriaXu]

Impressive!

[@oneinabillion654]

Shocking result. Thank you sir.

[@MichelvanBiezen]

Welcome 👍

[@Marco7873908727]

I don't understand something. Using formula: d=L sin ø Do I plug in the sine in radians or degrees? You used both and my gut tells me it's not right.

[@MichelvanBiezen]

It depends on the equation. The top equation is set up so that the angle is in radians.The bottom equation is a trig function and you use degrees for that equation.

[@Peter_1986]

Personally I always use radians for everything, unless degrees are significantly easier.

[@nathanyao1233]

Thank you Michel van Biezen

[@sawantsingh522]

Awesome explanation

[@garywybenga4188]

The moon rose at 82° that day. The sun rose at 80° 3 minutes after the moon. The sun set at 280° and the moon set about 20 minutes later at 283° So the moon was slightly south of the sun when the rose and slightly ahead. By the time they set the moon was further north of the sun and 20 minutes behind. The moon crossed the path of the sun just before the sun was going to pass it. That's why the shadow started southwest when the sun was approaching it but still north of it in latitude and moved north east as the moon crossed in front and the sun passed by to its south to make the shadow go north east

[@infoHazard-mg3ov]

3.05

[@MichelvanBiezen]

?

[@valentinotera3244]

..or 10 feet.

[@ManojKumar-cj7oj]

And its due to the size of aprature that gaves us this inability

[@harishankarkarthik3570]

Always love his bowties 😂

[@Pierrericheart]

Too much math bro. This makes no sense to someone who is not a calculus expert. You dont even explain what 1.22 is!

[@MichelvanBiezen]

Hi Pierre. You don't need to know any calculus to follow the information in the video, some simple algebra is sufficient. It is simply explaining the resolution a person has at various distances. The constant 1.22 in the algebraic equation can be calculated, but that calculation requires knowledge of differential equations and the Bessel function. Therefore at this level it is just simpler to call it a constant needed for the equation.

[@RayleighCriterion]

@@MichelvanBiezen I am curious where that 1.22 constant is used in similar equations and how it was derived.