I’ve never understood why manufacturers tell you to paint periscope faces blue. It’s probably due to the idea that they’re glass so they should look transparent, but it stands to reason that on the outside of the periscope, what you will see is the light coming out of the vehicle through the pericope. If the hatches are closed, or largely blocked by, say, a crewman, there will be very little light coming out and so the glass part of the periscope will be dark.
My way of painting periscopes is to normally paint them matt black. Yes, not gloss 
Once that has dried, I use an HB or 2B pencil to cover the whole glass part in graphite, which gives a sheen that changes depending on the direction from which you look at the periscope.
If the inner face is visible, I normally paint that white to show that there is a lot of light coming into the vehicle through the periscope.
And I’ve even been known to turn all of this upside down, for example for a periscope in an open hatch: if the outer side faces downward, not that much light will come through it, so paint the inner block dark and the outer one light (because it will emit the light falling onto the inner block that faces the sky).
Edit, slightly later
I thought, “This calls for an experiment to illustrate!”
Here’s a periscope:
To be precise, an American M6 type, as used in tanks like the M4 Sherman and many others:
Now, I happen to live in a house that has a screen door with a convenient cat flap (convenient for both the cat and for humans, who don’t have to open the screen door for the cat since I cut that hole in the door), just inside of which I set up the periscope and then covered it with a little footstool and a summer jacket that I use for spring and autumn because it’s much too warm for summer in these parts:
This blocks out the light on the inside, nicely simulating the periscope being mounted in a vehicle with its hatches closed. Now, going outside, what you see is this:
A dark face to the periscope. But lift up the jacket a little and take a peek on the inside:
