It's natural (but wrong) to think that the equations of SR tell you what light "experiences" if you just take the limit as the observer's speed approaches the speed of light. After all, light moves at the speed of light. However, there's a big mistake in doing this. In order to ask what light experiences, you would have to be riding along with the light and it would have to be stationary in your reference frame. SR assumes that no matter how fast you're going, light is always moving at the speed of light with respect to you.

More mathematically put, although you can take the limit as your velocity approaches the speed of light and get out answers, these answers can't describe what a photon sees, since you're still describing a frame in which the photon is moving at the speed of light.