Suppose I have a 32" and a 64" television. Now if I use SD dish connection(like Tata Sky) for both, I will get almost same same video quality on both, right? I was wondering how this is possible. I mean, any shows on TV are aired at 640x480 res(for SD), so why doesn't the video get distorted for a larger TV?

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The quality does differ. If both TVs have the same resolution and specs, the image on the bigger one will be more pixelated if viewed from the same distance. The last part of the sentence is the key. You will probably sit farther away from the 64" television. The recommended viewing distance increases proportionally in relation to the screen size (for example, here is a calculator).
If you watch the same source video from the same viewing distance on both TVs, you will notice more pixelation on the bigger one.

You can also notice this effect when looking at any (pixel-based) image on your screen. Open any image on your computer. Looks smooth? Good, then zoom in by a few hundred percent. Now you will notice pixelation to the point where you can make out the individual pixels. Conversely, if you have a pixelated image and zoom out enough, it will look smooth. The same thing happens when you move your chair farther away from/closer to your TV.

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