# 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. (Click on the image to see the full animation.)

The dolly zoom is an unsettling in-camera effect that appears to undermine normal visual perception. It is part of many cinematic techniques used in filmmaking and television production.

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 (or moves) towards 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 developed by Irmin Roberts, a Paramount second-unit cameraman, and was famously used by Alfred Hitchcock in his film Vertigo.

## Alternative names

A dolly counter zoom is also variously known as:

• The "Hitchcock zoom" or the "Vertigo effect"
• "Hitchcock shot" or "Vertigo shot"[1][2]
• Triple Reverse Zoom
• Reverse Tracking Shot
• Back Zoom Travelling
• "Smash Zoom" or "Smash Shot"
• Vertigo zoom
• A "Jaws shot"
• A "zido"
• A "zolly"
• Telescoping
• Trombone shot
• Push/pull
• The Long Pull
• The Trombone Effect
• A Stretch shot
• Reverse Pull
• 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 him or her to reassess everything he or she had previously believed. After Hitchcock popularized the effect (he used it again for a climactic revelation in Marnie), the technique was used by many other filmmakers, and eventually became regarded as a gimmick or cliché. This was especially true after director Steven Spielberg repopularized the effect in his highly regarded film Jaws, in a memorable shot of a dolly zoom into Police Chief Brody's (Roy Scheider) stunned reaction at the climax of a shark attack on a beach (after a suspenseful build-up).

## Optics

For most purposes, we can assume 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 $s_i$, the distance between lens and the object $s_o$, and the focal length $f$ are related by:

${1 \over s_i} + {1 \over s_o} = {1 \over f}$

The transverse magnification $M$ is related by

$M = {s_i \over s_o} = {f \over (s_o-f)}$

The axial magnification $M_{ax}$ of an object at $s_o$ is the rate of change of the lens-image distance $s_i$ as the lens-object distance $s_o$ 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:

$M_{ax} = \left | {d \over d(s_o)} {s_i \over s_o} \right | = \left | {d \over d(s_o)} {f \over (s_o-f)} \right | = \left | {-f \over (s_o-f)^2} \right | = {M^2 \over f}$

One can see that if magnification remains constant, a longer focal length results in a smaller axial magnification, and a smaller focal length 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. For example, a FOV of 90° and a distance of two meters yield a constant width of four meters, allowing a four-meter-wide object to remain still inside the frame during the effect.

$\mathrm{distance} = \frac{\mathrm{width}}{2\tan\left(\frac{1}{2}\mathrm{fov}\right)}$