# Bathroom Mirror vs Eye Lasers

There is this scene where the main good girl is fighting the big bad alone. The big bad fires his eye lasers at the good girl, who uses a bathroom mirror to reflect the rays. The big bad can control his saccades while firing his eye lasers, and his eyes and the surrounding tissue are sturdy enough to endure his use of eye lasers. And here are the stats on the lasers. They are circular beams that have a radius of 7.26 mm, and can heat an 1.7 m, 70 kg human up to a theoretical maximum temperature of 3000 K. Why I say that is because it takes far lower temperatures to cause major damage. If the big bad were to fire his eye rays at a human, he couldn't hope to heat them up more than 3000 K, and I will show you the math behind it.

First, there's the conduction of heat to outside the body. If we assume that the air temperature is 293 K, then the rate of conduction should be 1.12 MW, and the rate of radiation should be 8.34 MW, which would put the total energy loss at 9.46 MW. The flux from those beams would be 57.1 $$kW/mm^2$$, which is like standing 82.2 thousand km from the surface of the Sun, so they are powerful little buggers. And that's just the stats on one beam! Two fired over the same area? You're looking at a flux of 114 $$kW/mm^2$$, which is like being 2^.5 times closer to the sun. We're looking at if just one hit the mirror. We will assume that the mirror has an albedo of 78%, is made of silver-coated glass, and is 6.35 mm thick. We will assume that the mirror is made of borosilicate glass, which will break if there's a temperature difference of 165 K, and has a thermal conductivity of 1.2 $$W/(m*K)$$.

We will assume that the mirror starts at a temperature of 293 K throughout. How long could the mirror last against the eye laser?

• Any laser that can seriously injure a person will go right through a traditional mirror. It will probably go through a completely metal mirror. Commented Jan 19, 2021 at 23:36
• Mirrored surfaces dont reflect perfectly, you can assume about 10 to 20% of the light still being absorbed (I see you use 22%). This is a problem as it can burn the material, which reduces the reflectivity and aborb more which causes it to burn faster etc. Assuming the heating up happens rapidly then my guess is the mirror will burn if not vaporize, after which the good girl is either dead or wounded and now staring into the rest of the laser beams. Commented Jan 19, 2021 at 23:55
• Here's a YouTube video of a 500W laser effortlessly cutting a mirror: youtube.com/watch?v=p-VlVmBZGI4 Granted, the mirror is acrylic in this case but the mirror coating on glass isn't really going to fare much better. Commented Jan 20, 2021 at 0:04
• The cross-section of the beam is about 166 square millimeters. With a flux of 114 kW/mm², each beam carries about 19 MW. There are two beams, for a total of about 38 MW, of which about 7.5 MW are absorbed by the flimsy mirror. The specific heat of glass is about 700 J/kg·K. Assuming a 1 kg mirror, its temperature will go up by more than 10,000 kelvin per second... Those 165 K difference in themperature will be reached in about 15 milliseconds. Commented Jan 20, 2021 at 0:09
• She might do better with the hair spray. Commented Jan 20, 2021 at 4:17

Bathroom mirrors are not made with dielectric mirrors, since we don't want to see only our red or blue reflection. This means that out of the 114 $$kW/mm^2$$, 11 are being absorbed by the mirror.