Light having a wavelength of shines on a diffraction grating.$$ The third$-$order maximum is at an angle of $.$Residential solar panels have come down in price substantially in the past decade, and government incentives to install solar are not uncommon, so they are becoming more popular.$$ For some homeowners, it makes sense to install a battery storage system along with their solar to help make most efficient use of the energy they gather.$$ Consider three people, Amy, Ben, and Cassandra, who have installed solar on their roofs.$$ The maximum power output of each of their systems is as follows:

Amy:

Ben:

Cassandra:

All of these people also opted to install a battery storage system along with their solar.$$ The following are the storage capacities of each of their batteries:

Amy's battery:

Ben's battery:

Cassandra's battery:

Compute the time $($in hours$)$ it would take for each of these people to charge their battery from totally empty to totally full, and in the answer box, write the$$smallest$$of these times. How many lines $($slits$)$ does the grating have per centimeter?