**You Can’t See It**

Someone on a mailing list of friends asked about HDTVs the other day. I gave what is part of my standard answer. If you’re more than 2 feet away from the TV for each 10 inches of diagonal, 1080p is a waste of money. You can’t see it. Someone asked what I meant, so I wrote up the math. It’s worth sharing here… so that someone on the internet can tell me I’m wrong. I’m sure I forgot to multiply or divide by 2 somewhere. 🙂

Visual acuity is measured in arcminutes per line pair. 20/20 vision has an acuity of about 2 arcminutes per line pair. That means that for alternating pairs of black and white lines occupying a 1 degree angle of your field of view, you can see 30 pairs at 20/20 but 31 pairs would resolve into a bit of a gray mass.

What does that mean for your TV? If a pair of scanlines on your TV subtends an angle smaller than 2 arcminutes, then you likely can’t resolve them from each other. Your eye will average them together. Since the subtended angle is a function of your distance from the TV, the farther you are from the TV, the bigger your TV needs to be. Let’s do the trig on that.

2 arcminutes is .0333 degrees. For a pair of scanlines subtending an angle, theta, the following formula holds:

Tan(theta/2) = heightOfScanline / distanceFromTV.

For .0333 degrees, the minimum resolution, this means .000291 = heightOfScanline / distanceFromTV. Once we know the height of the scanline, we can calculate the maximum distance we can sit from that TV and see that scanline at 20/20 vision.

Next up, how tall is a scanline? It’s heightOfTV / 1080. Since widescreens are 16:9 aspect ratios, we can use simple trig to tell us. A TV can be divided into two right triangles with angles of 90, 60.6, and 29.4. By some trig,

heightOfTV = diagonalLength * sin(29.4).

So, our scanlines are:

heightOfScanline = diagonalLength * .49 / 1080

If we recombine all that, we get the following formula for the minimum TV size at a given distance to see 1080p. Just plug in about how far you are from the TV to know if it’s worth your cash.

diagonalLength = .641 * distanceFromTV

Hint: It’s likely not worth your cash to get 1080p.

**The Wasteland Beckons**

I’ve been playing Fallout 3 quite a bit. There’s plenty of reviews on the matter for you to read. I just wanted to give a public shout out to Bethesda. It’s a great game. I think they’ve really captured the spirit of the first two titles and brought them into this generation. There are some rough edges, particularly in the first hour, but I’m overall thrilled and impressed with the title. I’m really looking forward to the downloadable content as well since I’ll probably finish my playthrough around the time it drops.

*Thursday is the new Wednesday. dba*