The Submarine Periscope

Build the version everyone builds first, then find out exactly where it stops working.

1. Mount two flat mirrors at 45° facing each other at the ends of a cardboard tube, about 300 mm apart.
2. Look through it — it works well.
3. Now extend the tube to 1 m, then 2 m, keeping the same mirrors, and look again.
4. Record the apparent field of view and brightness at each length.

The field of view collapses as the tube lengthens. At 300 mm you see a useful scene; at 2 m you are looking down a straw. Nothing has changed except distance.

The reason is geometric rather than optical: the far mirror subtends a smaller and smaller angle as it recedes, so it collects an ever narrower cone of light. A plain tube's field of view is set by its length-to-diameter ratio, and a 9 m periscope of 180 mm diameter would show essentially nothing.

Demonstrate the fix at bench scale, with a single lens in a long tube.

1. Take the 2 m tube from step 1, where the view had collapsed to a pinhole.
2. Place a long-focal-length converging lens midway along it.
3. Adjust its position until the image at the eyepiece is sharp, and measure the field of view again.
4. Note whether the image is upright or inverted.

One lens transforms the useless pinhole back into a usable scene — and the image is now upside down. Each relay stage inverts, so an even number of stages comes out upright and an odd number does not.

That is why relay counts are chosen with the final orientation in mind, and why some designs add a deliberate erecting element. An inverted horizon in a combat instrument is not a quirk, it is a hazard, so the optical train is designed backwards from the requirement that the operator sees the world the right way up.

A periscope is also a rangefinder, using nothing but a graticule and known ship dimensions.

1. Etch or print a graticule with angular divisions and fit it at the eyepiece focal plane.
2. Calibrate it: view an object of known height at a measured distance and record the divisions it spans.
3. Now view the same object at unknown distances and compute range from the angle it subtends.
4. Repeat with the object's height deliberately misjudged by 20 percent and see what happens to the range.

Range comes out as height divided by the subtended angle, and it is only ever as good as your estimate of the height. That last test is the important one: a 20 percent error in assumed masthead height puts a 20 percent error straight into the range.

Which is why submarines carried recognition manuals listing masthead heights by ship class. Identifying the target correctly was not naval trivia — it was the measurement input, and misidentifying a ship meant mis-ranging it.

The periscope is the only part of a hidden boat that is not hidden, and it announces itself twice.

1. Draw a vertical rod through still water at a measured speed and photograph the surface disturbance.
2. Repeat at double the speed and compare the wake.
3. Note the length of the visible trail behind the rod in each case.

A raised periscope leaves a visible wake — the feather — and it grows dramatically with speed. A boat at periscope depth must therefore go slowly, which limits how quickly it can reposition, which is a tactical constraint imposed entirely by an optical instrument.

The second betrayal is radar: a thin vertical metal tube above the water is a small but perfectly detectable target, and airborne radar hunting periscopes was the single greatest threat to submarines by 1943.

So the whole design becomes a compromise about exposure. Minimum diameter, minimum time raised, radar-absorbent coatings, and eventually the attack periscope made deliberately thinner than the search periscope — accepting a dimmer, narrower view in exchange for being harder to see.