Distance-creating "lens"?

Question

On another recent question I noted that it's theoretically possible to take "short-range" pictures that have the perspective as if they were taken at a distance, by means of a system of mirrors:

To be fair, a "lens" could in principle create distance greater than any external dimension of the lens if it's actually a system of mirrors and lenses by bouncing light rays back and forth multiple times

with another user noting:

But only if the first refractive surface (or curved reflective surface), as opposed to flat reflective surfaces, is placed at the other end of all of those mirrors

Is there any commercially-available lens+mirror assembly to achieve such an effect? If not, are there any write-ups/tutorials on assembling something practical?

Here's an awful ASCII-art diagram of a possible design (shown as cross-section):

-------------------------------------------------------------\
/-----------------------------------------------------------\|
|/----------------------------------------------------------++---
|\----------------------------------------------------------/|
\------------------------------------------------------------/

where horizontal and vertical strokes indicate path of light inside the enclosure and diagonal ones are mirrors at 45-degree angles, with light entering from the top-left and exiting (to refractive lens stage) on the right. As drawn, it should add an effective 5x the length of the "lens" to the distance to the subject; to be of practical benefit it probably needs to be fairly long and/or have a few more loops but I didn't want the ASCII art to get any more unwieldy.

Answer 1

Increasing the apparent distance between camera and subject by using mirrors, as described in the question, cannot be done reasonably within a lens. However, mirrors can be used to increase apparent distances in limited space if a permanent installation is acceptable.

Flat Mirrors

With a single flat mirror, if subject and camera are the same physical distance from the mirror, the mirror will need to be half the size of the subject plus whatever background will be captured because the angle of reflection is equal to the incidence angle. This will double the apparent distance between camera and subject.

The size of the mirror can be decreased if it is moved closer to the camera than it is to the subject. But by doing so, the apparent distance between camera and subject will approach the actual distance, which would defeat the purpose of using mirrors in the first place.

Curved Mirrors

All lenses create and correct distortion, so any distortions created by curving mirrors are reversible. Curving the mirror can be used to decrease the physical distances while retaining the apparent distances. However, it does so at the expense of increasing mirror surface area.

As with flat mirrors, the farther the subject is from the mirror, the close the apparent distance will be to the actual distance, reducing the effectiveness of the contraption.

In Practice

A lot of mirror surface area would be needed. The ratio of distances won't work out to significantly alter perspective much better than taking a few steps back.

If a permanent installation is acceptable, what you'd end up doing is putting a large mirror on a wall. Then you would have to avoid capturing the camera in the frame, as well as keep the mirror clean. This is how some optometry/ophthalmology offices are set up to increase the "distance" between patients and eye charts in small rooms.

Decreasing Distance

Fiber optics has been used to do the opposite of what you ask to improve and save lives.

Answer 2

to be of practical benefit it probably needs to be fairly long and/or have a few more loops but I didn't want the ASCII art to get any more unwieldy.

This is the crux of the problem — it wouldn't just be the ASCII art that would be unwieldy. Even assuming perfect optics, at each "bounce", the mirror needs to be big enough to cover the entire field of view.

There's basically two situations where this would be useful: small rooms and selfies. I can't imagine a selfie stick holding this thing steady, so that's pretty much out. Small rooms... maybe more interesting, but you'd pretty much fill that room anyway. The one case where I can think of this possibly really being useful is in a fixed photobooth — the camera could be on the floor or near the ceiling, and a mirror in the back of the box at 45° could divert light from the subject to it. But, I don't think that'd likely be worthwhile with more than one mirror — and anyway, then we're not talking about something that attaches to the camera like a lens.

Answer 3

Every "bathroom mirror selfie" ever taken uses such a mirror. By holding the camera three feet from a mirror the user places an optical distance of six feet between themselves and the camera they are holding in their hand.

Is there any commercially-available lens+mirror assembly to achieve such an effect?

There are commercial systems made to be used with what are effectively the 'reciprocal' of camera lenses. They are made to be used with short throw projectors.

I'm not aware of any such system made for lenses used in "creative photography" that is covered within the scope of this site. There may well be some such designs used for machine vision in manufacturing environments, but that is mostly beyond the scope of this community.

Answer 4

If you do a simple thought experiment about how your location in space affects the way things look (eg. how perspective makes things close to you look bigger), Imagine a wall (in black) in front of a subject (red ball), if your eye / sensor is close to the wall, there's no way for light to bend around the wall and get into your sensor. however if you take a step back, it will show on the edges (since the ball is actually bigger, and perspective approaches orthographic as the distance increases towards infinity)

In order to be able to 'see' what the eye would see from a distance, you would need a contraption that could 'reach out and capture + rediret' the light rays back down to the eye. in other words, a really big lens, maybe one that's almost as big as the wall / obstruction (in this example), and the further away you want to be, the bigger the lens. If you imagine the lines approaching parallel at infinity, then the lens would have to be as big as the subject you're trying to take a picture of in order to take an 'orthographic' picture.