A Divorce actually has very little effect on your rights in your spouse's/ex-spouse's Social Security benefits.
So long as the marriage lasted ten years, a spouse who has not worked or who has low earnings can be entitled to as much as one-half of the retired worker’s full benefit.
If you are eligible for both your own retirement benefits and for benefits as a spouse/ex-spouse, Social Security always pays your own benefits first. If your share of your spouse's/ex-spouse's benefits are higher than your retirement benefits, you will get a combination of benefits equaling the higher spouse benefit.
The amount of your spouses/ex-spouses benefit that you receive has no effect on the amount of benefits that they receive.
To see a more complete explanation visit this helpful Social Security website.