A Wi-Fi connection indicator does not guarantee that a web page, mail service or stream can reach the internet. When the Mac is connected to the intended network but those tasks fail, collect evidence while the symptom is present.

Note the time, network name, location and which task failed. If another device is available, record whether the same service works there without turning that comparison into a confirmed diagnosis. Avoid changing several router and Mac settings before preserving the original conditions.

Run the built-in analysis

Apple’s Wireless Diagnostics guidance covers this connected-but-not-working situation. Save your work, quit open applications as instructed and make sure the Mac is joined to the affected Wi-Fi network.

Hold Option while opening the Wi-Fi menu and choose Open Wireless Diagnostics. Follow the assistant. Apple states that the tool analyses the connection without changing the network settings. Read the summary and use its information buttons for the documented explanations.

Keep a note of the result and when it was collected. A report made after moving to another network or after the problem disappears describes a different state, which may still be useful if clearly labelled.

Locate and handle the diagnostic archive

Apple places the generated archive in /var/tmp with a name beginning WirelessDiagnostics and ending .tar.gz. In Finder, use Go, Go to Folder to reach that location and identify the file associated with your test.

Preserve that archive and your observation note together. Diagnostic archives can contain detailed information about the computer and surrounding network conditions, so use an agreed private support route rather than making the file publicly accessible.

Do not repeatedly reset the router or delete network settings merely because the report contains unfamiliar terms. Ask the network administrator or support contact to interpret the relevant result in the context of the affected service.

When a change is agreed, repeat the original web or mail task and record whether it now succeeds. The acceptance check is the real connection behaviour; producing an archive alone does not prove that the Wi-Fi hardware or internet service has been repaired.

References: Apple: Wireless Diagnostics.