When attached to older TVs that do not support Extended Display Identification Data (EDID) version 2.0, the TV does not provide needed resolution data to the Adapter. EDID 2.0 was introduced in September 2006, so a TV older than 10 years or so will not be compatible.
Choose Apple menu > System Preferences, then click Displays. If your Mac doesn't recognize a display you've just connected, hold down the Option key to make the Detect Displays button appear, then click that button.
