The good ship Collateral Damage becomes aware of an incoming hostile missile. Collateral Damage has a laser cannon with a ten meter radius mirror operating on a mid-infrared wavelength of 2700 nanometers (0.0000027 meters). The divergence angle is (1.22 * 0.0000027) / 10 = 0.00000033 radians or 0.000019 degrees.
The laser cannon has an aperture power of 20 megawatts, and the missile is at a range of four megameters (4,000,000 meters). The beam brightness at the missile is 20 / (π * (4,000,000 * tan(0.000019/2))2) = 15 MW/m2 or 1.5 kW/cm2.
If the missile has a "hardness" of 10 kilojoules/cm2, the laser will have to dwell on the same spot on the missile for 10/1.5 = 6.6 seconds in order to kill it.
Figured another way, at four megameters the laser will have a spot size of 0.66 meters in radius, which has an area of 1.36 square meters. The missile's skin has a hardness of 10 kilojoules/cm2 so 13,600 kilojoules will be required to burn a hole of 0.66 meters radius. 20 megawatts for 6.9 seconds is 13,600 kilojoules. 6.9 seconds is close enough for government work to 6.6 seconds.