Final answer:
The law that allowed African Americans to serve in the army in 1862 was the Second Confiscation and Militia Act, which was authorized by President Lincoln. However, it wasn't until 1863 that President Lincoln started utilizing this authority.
Step-by-step explanation:
The law passed by Congress in 1862 that allowed African Americans to serve in the army was the Second Confiscation and Militia Act. This act authorized President Lincoln to enlist African Americans into the military for any purpose he deemed necessary for the public welfare. However, it wasn't until the Emancipation Proclamation was issued in 1863 that President Lincoln began taking advantage of this authority.