Can wifi signal reception be improved by opening a door? Use Case
A wifi user is in a different room than the router. The computer is having a hard time connecting and receiving the wifi signal.
Engineering Question
Can the wifi signal from the router to the computer be improved by opening a door to the room where the computer is?
Physics Question

Please describe the electromagnetic field equations (including refractive indices of doors and walls) at play in the engineering question and whether you believe opening a door will affect these equations as it relates to field strength of the wifi signal at the computer. See this article for inspiration.

http://www.electronicproducts.com/Passive_Components/Antennas/Apartment_Wi_Fi_connectivity_mapped_using_physics_and_math.aspx
Field Equations

(Differential Form)





 A: If the WiFi antenna is emitting at 2.4 GHz, you could detect a slight improvement of the signal, but unless the door is solid and very thick, I doubt it will make much difference. If it is emitting at 5 GHz the improvement could be bigger, as the wavelength is reduced and the door appears "bigger" to the electromagnetic wave.
Finally, if your antenna uses the very new 802.11ad standard (though I doubt it), emitting at 60 GHz, you wouldn't want to put the emitter at a different room than your receiver.
In general, electromagnetic scattering is very dependent on the size of the scatterer relative to the wavelength $\lambda$ of the wave. In sub lambda scatterer sizes we are in the "Rayleigh" regime, where particles (or doors, or walls...) cause some dispersion but the waves are not much affected by them (consider the case of FM radio emission: the wavelengths are so large that the difference in reception inside/outside a building is not noticeable; the walls are transparent to the EM wave); in the lambda and sup-lambda regime, you need the full description of scattering from Maxwell's equations (as in "Mie" scattering) to get an accurate description of the process, but roughly speaking, particles (resp. doors, walls...) block (at least partially) the wave. 
In WiFi emission you are stuck in a mesoscale with dimensions of the order of $\lambda$, so you can be in one regime or another depending on the frequency of emission.
A: 
Can the wifi signal from the router to the computer be improved by opening a door to the room where the computer is?

Not too much.
You can put your laptop 2 meters away from a door, exactly in front of it, while the router is on the other side of the door also 2 meters away. You will see that with the door opened or closed the signal received by your computer has about the same quality. 
