If the logical test in an IF function is FALSE, the following happens:

* The function will ignore the `value_if_true` argument (the value you specified to return if the test is TRUE).
* If a `value_if_false` argument is provided (it's optional), the function will return that value.
* If no `value_if_false` argument is provided, the function will return an empty string ("").

Here's a breakdown for clarity:

Scenario 1: value_if_false argument provided

```
=IF(A1 > 10, "Value if True", "Value if False")
```

- If A1 is greater than 10 (TRUE), the function returns "Value if True".
- If A1 is less than or equal to 10 (FALSE), the function returns "Value if False".

Scenario 2: value_if_false argument omitted

```
=IF(A1 > 10, "Value if True")
```

- If A1 is greater than 10 (TRUE), the function returns "Value if True".
- If A1 is less than or equal to 10 (FALSE), the function returns an empty string ("").

In conclusion, the `value_if_false` argument is not required, but it allows you to specify a specific output when the logical test fails. If omitted, the function defaults to an empty string.