NavList:

Suppose we have two ordinary thin spherical lenses,
one positive, another negative of the same focal length.
Say one +1 another -1. And suppose that their axes coincide,
so that the lenses are parallel, at some small distance one from another.
This arrangement does almost nothing to the light rays.

Now displace one length by certain amount h PERPENDICULARLY to the axis.
So that the axes remain parallel, but the distance between them is now h.

What will this system to do the rays?
It turns out that the parallel rays will come out parallel, but
their direction will change by a small angle which is proportional to h.

This is the principle used in Soviet dipmeter.
My question to those who know something about optical devices:
did you know this?
Is this used in any device that you know?
(I am certainly not an expert in optics:-)

First I was surprised. Then I proved it for cylindrical lenses.
Then I told to Bill Morris, and he immediately made an experiment
confirming the phenomenon. I had some doubts that this is correct
for spherical lenses (rather then cylindrical), but today I figured out
a methematical proof.
So I withdraw my statement that the lenses in the dipmeter are
"probably cylindrical". They are probably ordinary spherical lenses.

So if you need to bend a ray by a SMALL angle, you do not have
to use rotating mirrors and prisms, but can use two odrinary
lenses instead. I am almost certain that Soviet stadimeters which
can be seen on e-bay work on the same principle.
(Their official purpose is "to maintain order and distance
in a column or convoy").

The dipmeter working on this principle was described to the List in detail
recently, it is extremely simple and needs no adjustment.
So they could just hermetically seal the case.

I also found something about the inventor: Vladimir Vladimirovich
Kavraiskii, 1884-1954, engineer, rear admiral; besides the dipmeter he
is remembered for "Kavraiskii map projection". Winner of the Stalin Prize.
Here is the ship named after him:
http://navsource.narod.ru/photos/06/395/06395001.jpg

Alex.

----------------------------------------------------------------
NavList message boards and member settings: www.fer3.com/NavList
Members may optionally receive posts by email.
To cancel email delivery, send a message to NoMail[at]fer3.com
----------------------------------------------------------------