Why doesn't light bend in a box travelling at constant velocity like in an accelerated box? If a box is accelerating in x direction and if a photon comes from the y direction then its entry and exit point will not lie in the same line that is the the path of the photon is curved because at the point of entry and exit is of photon the box has moved certain distance.
But if this happens for an acceleration box why don't it happen with a a box with zero acceleration that is with constant velocity? Since in both cases the the box is moved forward during the time the photon is inside the box. 
 A: If the box is moving at a constant speed in the x direction and the light beam is moving in the y direction, then the path of the beam will be straight but tipped relative to the box, before and after entering the box. (A telescope must be aimed slightly away from its object star to compensate for the motion of the earth.)  If the box is accelerating then some one inside would see the beam go from straight to curved. In both cases the x coordinate for the entry point (as measured in the box) will be greater than the x where the beam hits the far wall. 
A: Yes, if we consider a box with proper acceleration then the path of light is curved within the box. This is because the velocity of the box increases during the light transverses the box.
In contrast if the box moves with constant velocity then the path of the light is straight (no increase of velocity).
Imagine the light moves perpendicular to the motion of the box. The bottom of the box moves upwards with constant velocity. So the distance between the light and the bottom decreases with constant velocity. Therefor the path of the light is straight and a bit downwards towards the bottom.
A: If the light originated from inside the box, then it has the same constant motion in the x direction as the box does. There is no relative motion between the light and the box, they both move together. Thus, it remains straight for constant velocity. 
