Calculate the minimum number of lines required on the encoder disk if an optical incremental encoder is to be used?

I can't tell what needs to be done based on what you have written.

The minimum number of lines is 1 which gives you one pulse per revolution unless there are hidden requirements not made clear to me by what you wrote.

What is the 10 ms limit for example? Is that how often the system can check the encoder pulse output? Or, maybe are you building an encoder which will count pulses and send a report of the number of pulses once every 10 ms.

If the shaft velocity is to be calculated based on the number of pulses reported each 10 ms and you need 10% accuracy then that could be used to determine the minimum number of lines needed. Since the error in the count is +- 1 pulse per count you would need at least 10 pulses for each 10 ms window to produce that accuracy. Which means you would need 1000 pulses per second when the shaft was turning at it's slowest speed. The slow speed is 1 revolution per second (60 rpm) so you would need a minimum of

Or, you could argue that the average error was +- 1/2 pulse, making the needed count 500 lines to produce an average error of 10%.

But, if you were producing a device to accurately measure the time between each encoder pulse, you could calculate a new velocity with each pulse. If you wanted to be able to produce a new updated shaft velocity value each 10 ms, then you need 100 pulses per second or 100 lines on the encoder wheel.

But if the lines to non-line spacing on the encoder is 50%/50% then you don't need 100 lines, you only need 50 lines which would give you 100 state changes.

In short, you didn't tell me enough to know what it is you are really asking. The answer could be somewhere from 1 to 1000 lines.