The next day, I took some pictures of the clock. This picture is my view of the clock when I was sleeping.
As you can clearly see, glare from outside blocks my view of the clock's hands.Now I move a little closer and it becomes clearer.

Moving even closer makes even more of the clock visible

And being right by it makes it completely clear

Because of the glare off of the clock, I was late. The reason the glare is reduced as I move closer to the clock is that the angle from the light source outside to my eyes changes. The outside light directly hits the clock face and bounces off of it into my eyes when I'm farther away. As I get closer, the angle of incidence between the clock and I changes and the light less and less directly hits the clock and more and more of it becomes visible. The glare is actually polarized light that vibrates in a vertical direction. If I had been wearing polarized sunglasses, I would have been able to see right through it. This very unfortunate incident, upon further inspection, was one that an understanding of physics helps resolve.
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