Would you mind if I opened the window?

[Snappy_is_here]

"Would you mind if I opened the window?" is found for the usage of the word "mind" in Longman Dictionary of Contemporary English. The dictionary explains that it is spoken and used when making a polite request.In the same dictionary, "Would you mind if I open a window?" is also found for the usage of the word "mind."
Are these both acceptable and the same in meaning?
"Would you mind if I opened the window?"
"Would you mind if I open the window?"

 

[Michel09]

They have the same meaning : being polite to someone when making a request. The only difference between the two is that the verb "open" is in a different form.

 

[natkretep]

'Would you mind if I opened the window?' is fine and normal. I was not sure about the second version, but on reflection, I think it's also possible, with no difference in meaning. I'm less likely to use that version. I tried to change the verb so that the difference is obvious:

Would you mind if my son left early?
Would you mind if my son leaves early?
Would you mind if my son leave early? (subjunctive)

 

[Cagey]

I agree with natkretep.

However, if you do a dictionary search for would you mind if I, you will find several threads on the construction, with varying opinions on whether the present (open) is acceptable.

 

[Lagrangepoint]

To borrow natkretep's example;
I would use the present tense only with 'Do' and the past tense with 'Would' as follows:

Do you mind if my son leaves early?
Would you mind if my son left early?