Question

very optical device has an angular resolution, the smallest angle over which it allows us to tell if two dots -- or two stars -- are distinct. If two stars have an angular separation less than the angular resolution, they appear as as a single object.

This limited angular resolution can arise for a number of reasons: quality of the optics, blurring of the atmosphere and quantum mechanics. For example, from the ground on Earth, due to the blurring of the atmosphere, the best optical telescopes have an angular resolution of 0.5 arcsecond. From the Hubble Space Telescope, the angular resolution is limited by quantum mechanics (diffraction) to about 0.10 arcseconds, about 5x sharper than from the ground.

a) The human eye is also an "optical device" and so also has an angular resolution. People with perfect eyesight have an angular resolution of 0.6 arcminutes. Quite a while ago, Apple has claimed that its iPhone 4 had a "retina display'', by which it meant that the pixels on its phone would appear smaller than the angle an eye could resolve. This iPhone had a display with 326 pixels per inch. If the phone is held a foot away from the eye, is this claim true?

Large screen TVs (say 60 inches measured across the diagonal) have 1920 pixels across by 1080 pixels down at HD resolution. How far away from such a TV do you need to sit to get a "retina" TV display?

Answer 1

A) With 326 pixels per inch the spacing between two pixels is = 1/326 inch

Now for small angle approximation we can say that tan Θ = Θ when it is expressed in radians.

So the angle that it creates with the eye is , 1/326 inch / 12 inch ~ 0.000255rad = 0.8788arcminutes.

This is resolvable by human eye from a distance of 1feet. The claim is not true.

_________________________________________

The aspect ratio of the TV = 1920:1080 = 16:9 = 1.777 : 1

If the diagonal is 60 inches then the length of the panel is =

Now the pixel separation is = 52.29 / 1920 = 0.0272"

In order to simulate a retina display, the distance between the screen and the observer is x inches (say).

Now the equation is,