9464

The Headlight Effect

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)

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

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

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

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+