Why does my dusk to dawn light go off when the furnace kicks in?
Understanding the problem
Think of your wiring like a pipe full of water, and each device like a pump. Each pump draws a specific amount of water, but not necessarily the same amount as any of the other pumps, and the water in the pipe can only be supplied at a fixed rate.

When the light turns on, it &quot;pumps&quot; a small amount of water from the supply pipe. This amount is far less than the pipes supply rate, so there is no problem.

When the furnace comes on, it &quot;pumps&quot; a huge amount of water (for a short time). This amount is close to, or greater than the amount of water in the supply pipe. This means there is less water in the pipe for the light, so the light cannot function properly.

This is an over simplified, and arguably inaccurate analogy.
Solving the problem
First off, Having the light on the same circuit as the furnace is not correct. This should be fixed as soon as possible, and will likely solve the problem you are seeing.
This could be an indication that one of the components of the furnace is reaching the end of its life, and needs to be serviced.   High current draws in an appliance are commonly caused by motors. Motors will draw more current while starting than they do when they are running, this is known as inrush current and can quite a bit higher than the devices full-load current.  This large current draw during start-up can be increased if additional force is needed to get the motor spinning, for example if the bearings are going bad.  You'll want to inspect the furnace, and pay close attention to any motors.  Make sure they are properly greased, and working normally.
If this has always been an issue all along, the furnace is probably operating normally and there is nothing to worry about.  If this has only become an issue recently, you may want to inspect your furnace (or have a professional inspect it).