Choosing a TV for yourself, your loved one, from the standpoint of science, not advertising

Hello.

I was prompted to write this short article by a dispute regarding the choice of TV.

Now in this area - as well as in “megapixels for cameras” - there is a marketing bacchanalia in the pursuit of resolutions: HD Ready has long been replaced by Full HD, and 4K and even 8K are already becoming increasingly popular.

Let's figure it out - what do we really need?

A school geometry course and some basic knowledge from Wikipedia will help us with this.

So, according to this very Wikipedia, the naked eye of the average person is a unique device that is capable of simultaneously viewing space at an angle of 130°-160°, as well as distinguishing elements at an angle of 1-2′ (about 0,02°-0,03°). Wherein Fast focusing occurs at a distance of 10 cm (young people) - 50 cm (most people 50 years and older) to infinity.

It looks cool. In fact, it's not that simple.

Below is the field of view of a person’s right eye (perimetric card, numbers on the scale are angular degrees).

The orange spot is the projection site of the fundus blind spot. The field of vision of the eye does not have the shape of a regular circle, due to the limitation of gaze by the nose on the medial side and the eyelids above and below.

If we superimpose the image of the right and left eyes, we get something like this:


Unfortunately, the human eye does not provide the same quality of vision across the entire plane at a wide angle. Yes, with two eyes we can recognize objects within a coverage of 180° in front of us, but we can recognize them as three-dimensional only within 110° (to the green zone), and as full-color ones - in an even smaller range of about 60°-70° (to the blue zone). Yes, some birds have a field of view of almost 360°, but we have what we have.

Thus we get that a person receives the highest quality image at a viewing angle of about 60°-70°. If greater coverage is needed, we are forced to “run” our eyes across the image.

Now - about TVs. By default, consider TVs with the most popular width-to-height ratio as 16:9, as well as a flat screen.

That is, it turns out that W: L = 16:9, and D is the screen diagonal.

Hence, recalling the Pythagorean Law:


So, assuming that the resolution is:

• HD Ready 1280x720 pixels
• Full HD has 1920x1080 pixels
• Ultra HD 4K has 3840x2160 pixels,

we find that the pixel side is:

• HD Ready: D/720,88
• Full HD: D/2202,91
• Ultra HD 4K: D/4405,81

Calculation of these values ​​can be found here

Now let’s calculate the optimal distance to the screen so that the eye covers the entire image.

From the figure it is clear that


Since the largest parameter of the height and width of the picture is the width - and the eye needs to cover the entire width of the screen - let's calculate the optimal distance to the screen, taking into account that, as shown above, the viewing angle should not exceed 70 degrees:

That is: In order for the eye to cover the entire width of the screen, we must be at a distance no closer than approximately half the diagonal of the screen. Moreover, this distance must be at least 50 cm to ensure comfortable focusing for people of any age. Let's remember this.

Now let’s calculate the distance at which a person will distinguish the pixels on the screen. This is the same triangle with the tangent of the angle, only R in this case is the pixel size:

That is: at a distance greater than 2873,6 pixel sizes, the eye will not see grain. This means, taking into account the calculation of the pixel side above, you need to be at the following minimum distance from the screen for the picture to be normal:

• HD Ready: D/720,88 x 2873,6 = 4D, that is, four screen diagonals
• Full HD: D/2202,91 x 2873,6 = 1,3D, that is, approximately a little less than one and a half screen diagonals
• Ultra HD 4K: D/4405,81 x 2873,6 = 0,65D, that is, slightly more than half the screen diagonal

And now what it all led to -

Conclusions:

1. You should not sit closer than 50 cm to the screen - the eye will not be able to focus on the image normally.
2. You should not sit closer than 0,63 screen diagonals - your eyes will get tired because they will have to run around the picture.
3. If you plan to watch TV at a distance greater than four screen diagonals, you shouldn’t buy something cooler than HD Ready - you won’t notice the difference.
4. If you plan to watch TV at a distance greater than one and a half screen diagonals, you shouldn’t buy something cooler than Full HD - you won’t notice the difference.
5. Using 4K is only advisable if you look at the screen at a distance of less than one and a half diagonals, but more than half a diagonal. Probably these are some kind of computer gaming monitors or giant panels, or a chair standing close to the TV.
6. Using a higher resolution does not make sense - you will either not see the difference with 4K, or you will be too close to the screen and the viewing angle will not cover the entire plane (see point 2 above). The problem can be partially solved with a curved screen - but calculations (more complex) show that this gain is extremely doubtful.

Now I recommend measuring your room, the location of your favorite sofa, the diagonal of the TV and thinking: does it make sense to pay more?

Source: habr.com