# The Headlight Effect

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows how nine light rays (emitted at angles from to in steps in the rocket frame) are measured by the laboratory observer as the rocket flies past at speed .

Contributed by: Paul A. Nakroshis (Department of Physics, University of Southern Maine, Portland, ME) (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

A standard problem in special relativity asks you to consider light emitted uniformly in all directions from both the rocket frame (where the light is emitted from) and the laboratory frame (watching the rocket fly past). From the point of view of an observer in the laboratory frame, the light emitted from the rocket frame (in the forward hemisphere) is measured to be compressed into a cone in the forward direction. In the rocket frame, a particular light ray is emitted at an angle θ' such that

.

Such a ray will be measured to have a different angle, , in the laboratory frame, defined by

.

Then use the Lorentz transformations , to replace and , yielding

,

or, more simply,

.

To visualize this effect, define a ray as , where the slope, , is given by the tangent of the angle .

## Permanent Citation