It seems your dad has done something wrong. That is a difficult situation for a kid, whatever age, to process.
We learn from our parents. From infancy we look to them to be our strength, our protectors, our role models.
To discover they have human flaws leaves a lot of feelings which may include confusion, vulnerability, disappointment, even anger and resentment.
It is tough to learn a parent has done something wrong, especially when that wrong may possibly victimize other family members. There can be doubts, and fear.
Parents are flawed. We are human, and none of us are perfect. Discovering that is tough oftentimes for our kids.
Perhaps your mom knows, and is hurt by it, but hasn’t made a big deal of it in hopes of maintaining family unity.
I think if you approach your dad it puts that family unity in jeopardy.
However, if you feel you must have answers, I would not have the picture in hand. That would just involve an extra element of vulgarity not necessary.
If you feel you must have answers, simply refer to the picture. He would know what you mean. Ask him what this means for yourself and your family.
Since your father and the woman were both in the photo, that means the possibility someone else was there. I don’t know what resources your parents have, but it says to me possibly your mother knows, and hired an investigator to get proof.
Again I urge you to leave things alone. It could be a situation which has been dealt with already, and put into the past.
Look at it this way, if you had a girlfriend, and loved her deeply, would you want your parents to get involved if a problem came up between you?