# Dolly zoom

A computer-generated representation of a dolly zoom
A frame from an animation showing a dolly zoom being performed. At the top of the image is the camera's view; the cubes stay the same size as the teapots in the background grow bigger. At the bottom of the image is a plan view showing the camera moving back while zooming in, illustrating how the effect is achieved.
In the video inset, the object moves with the camera and it does not zoom, so the FOV does not change; thus there is no dolly effect

The dolly zoom is an in-camera effect that appears to undermine normal visual perception.

The effect is achieved by zooming a zoom lens to adjust the angle of view (often referred to as field of view, or FOV) while the camera dollies (moves) toward or away from the subject in such a way as to keep the subject the same size in the frame throughout. In its classic form, the camera angle is pulled away from a subject while the lens zooms in, or vice versa. Thus, during the zoom, there is a continuous perspective distortion, the most directly noticeable feature being that the background appears to change size relative to the subject.

The visual appearance for the viewer is that either the background suddenly grows in size and detail and overwhelms the foreground, or the foreground becomes immense and dominates its previous setting, depending on which way the dolly zoom is executed. As the human visual system uses both size and perspective cues to judge the relative sizes of objects, seeing a perspective change without a size change is a highly unsettling effect, often with strong emotional impact.

The effect was first conceived by Irmin Roberts, a Paramount second-unit cameraman, in Alfred Hitchcock's film Vertigo.[1]

In addition to its use in Vertigo the shot has been used in many other films, including Goodfellas,[2] Road to Perdition, Poltergeist, Jaws, Body Double, The Island of Dr. Moreau (1996 remake of the 1977 film), the Lord of the Rings films, Just Friends, and Josie and the Pussycats.[3]

## Alternative names

A dolly counter zoom is also variously known as:

• Focus disturbance zoom
• A "zido"
• A "zolly"
• Hunter Smith Shot
• "Hitchcock shot" or "Hunter shot"[4][5]
• The "Hitchcock zoom" or the "Vertigo "[3]
• Vertigo zoom
• Vertigo effect
• A "Jaws shot"
• Reverse Tracking Shot
• Triple Reverse Zoom
• Back Zoom Travelling
• "Smash Zoom" or "Smash Shot"
• Telescoping
• Trombone shot
• Push/pull
• The Long Pull
• Reverse Pull
• The Trombone Effect
• A Stretch shot
• More technically as forward zoom / reverse tracking or zoom in / dolly out
• Trans-trav (in Romanian and Russian), from trans-focal length operation and travelling movement
• Contra-zoom

## Purpose of the effect

The dolly zoom is commonly used by filmmakers to represent the sensation of vertigo, a "falling-away-from-oneself feeling" or a feeling of unreality, or to suggest that a character is undergoing a realization that causes them to reassess everything they had previously believed. Alfred Hitchcock popularized the effect, and he used it for a climactic revelation in Marnie.

## Optics

For most purposes, it can be assumed that the image space and the object space are in the same medium. Thus, for an object in focus, the distance between the lens and image plane ${\displaystyle s_{\text{i}}}$ , the distance between lens and the object ${\displaystyle s_{\text{o}}}$ , and the focal length ${\displaystyle f}$  are related by

${\displaystyle {1 \over s_{i}}+{1 \over s_{o}}={1 \over f}.}$

Then the transverse magnification is

${\displaystyle M={s_{\text{i}} \over s_{\text{o}}}={f \over (s_{\text{o}}-f)}.}$

The axial magnification ${\displaystyle M_{\text{ax}}}$  of an object at ${\displaystyle s_{\text{o}}}$  is the rate of change of the lens–image distance ${\displaystyle s_{\text{i}}}$  as the lens–object distance ${\displaystyle s_{\text{o}}}$  changes. For an object of finite depth, one can conceive of the average axial magnification as the ratio of the depth of the image and the depth of the object:

${\displaystyle M_{\text{ax}}=\left|{d \over d(s_{\text{o}})}{s_{\text{i}} \over s_{\text{o}}}\right|=\left|{d \over d(s_{\text{o}})}{f \over (s_{\text{o}}-f)}\right|=\left|{-f \over (s_{\text{o}}-f)^{2}}\right|={M^{2} \over f}.}$

One can see that if magnification remains constant, a longer focal length results in a smaller axial magnification, and a smaller focal length in a larger axial magnification. That is, when using a longer focal length while moving the camera/lens away from the object to maintain the same magnification M, objects seem shallower, and the axial distances between objects seem shorter. The opposite—increased axial magnification—happens with shorter focal lengths while moving the camera/lens towards the object.

### Calculating distances

To achieve the effect, the camera needs to be positioned at a certain distance from the object that is supposed to remain still during the dolly zoom. The distance depends on how wide the scene is to be filmed and on the field of view (FOV) of the camera lens. Before calculating the distances needed at the different fields of view, the constant width of the scene has to be calculated:

${\displaystyle {\text{distance}}={\frac {\text{width}}{2\tan \left({\frac {1}{2}}{\text{FOV}}\right)}}.}$

For example, a FOV of 90° and a distance of 2 meters yield a constant width of 4 meters, allowing a 4-meter-wide object to remain still inside the frame during the effect.

## References

1. ^ Lyttelton, Oliver; Lyttelton, Oliver (2012-05-09). "5 Things You Might Not Know About Alfred Hitchcock's Masterpiece 'Vertigo'". IndieWire. Retrieved 2017-02-01.
2. ^ This Is How A Dolly Zoom Works-Fandor on YouTube
3. ^ a b Wickman, Forrest (January 21, 2014). ""The Evolution of the Dolly Zoom," in One Supercut". Slate.
4. ^
5. ^ "The "Vertigo shot" and the oneiric frame". Archived from the original on 2007-09-15.