price difference in Stop limit order for option trading

If you want out at $10, I'd suggest that you make your stop price a bit higher. Bear in mind that because this is a limit order, you need some room between your stop and limit prices because that's your window for execution. If it's too narrow, the order is less likely to fill.

I tried in Interactive Broker, but the system told me the limit price cannot be too far from the stop price. I don't know how far is too far. That is why I am asking.

Check your default settings. IBKR has some settings that help to reduce fat finger trades. For example, you might have a preset limit of say 500 shares per order or say 10 option contracts. I have reconfigured mine to my trading limits. Note that if an order exceeds such a limit, it adds another screen step where you can override and transmit or cancel. I use these.

Perhaps your inability to place your limit order is because of a changeable default setting such as the above or perhaps that's just the way it is (IBKR policy). If it's the former, go into Configure Settings. Or if you wish, call tech support.