Mass of Box A vs Box B with Photon Inside

[JasonWuzHear]

Imagine you have two boxes, each with a photon of equal frequency inside the boxes. The boxes, however, have different side lengths (yet, the boxes on their own are equal in mass).

Wavelength of photon << Length of Box A < Length of Box B

I've seen that a photon increases the mass of the boxes. Do these boxes with the photon inside have the same mass?

I was thinking that if you make the box very very large, then photon bounces become less frequent, almost to the point where there will be long periods where the photon has not bounced inside. This would make it look like the larger box has less of 'something'.

 

[rootone]

My guess is as follows, but I'm prepared to be contradicted:

In the case of both boxes, while the photon is bouncing around, (in existence), it hasn't increased the mass of the box.
The mass of the box only increases if the photon becomes absorbed by the box material instead of being reflected.
I don't think the size of the box makes any difference to that increase, however the energy of the photon (it's wavelength) does make a difference.

 

[PAllen]

If you define the 'mass of the box' to mean mass excluding contents, then, obviously, neither box changes mass until the photon has an inelastic interaction with a box. However, for the mass of the system of box plus photon, the two masses are identical, and bouncing is irrelevant.